The Endgame Tutorial



1.
[{B:40/3kp3/8/3K4}{QB:1. In this position, does Black want to go first or second?{W:10_01}{A:Be3e2}{H1:e2}{W:10_01a}{A:Wd1e1}{H1:e1}{W:10_01b}
;1... e3-e2+;
{B:40/3kp3/8/3K4}{S:e3e2}{W:10_01I}Incorrect. Black doesn't want to move first, because then he'd have no better than a draw. Either he would have to check, 1... e3-e2+, or move his king to the side, which doesn't get anywhere. The check leads to an immediate draw. After White's king blocks the pawn, {S:d1e1}{W:10_01Ia}2. Kd1-e1, Black would have to move his king either to e3 {A:Bd3e3}{N1:e3}{W:10_01Ib}(2... Kd3-e3), giving stalemate, or away from the pawn {R}{C}{S:d3d4}{W:10_01Ic}(say 2... Kd3-d4), abandoning it all together. White could then capture the pawn {S:e1e2}{W:10_01Id}(3. Ke1xe2) and the game would conclude at this point, for neither side possesses sufficient mating material (enough material to force mate regardless what the opponent does). If in the above position advancing the pawn to the 7th rank gives check, as a rule the game is drawn. The position is winning, however, if the pawn moves to the 7th rank without giving check, for then the opposing king is forced off the home rank and there's no stalemate. Nor, in the given position, does moving the king away from the promotion area {B:40/3kp3/8/3K4}{S:d3d4}{W:10_01Ie}(say 1... Kd3-d4) help either. White simply moves his king to {A:Wd1e1}{A:Wd1e2}{N1:e1e2}{W:10_01If}e1 or e2, staying on the same file as the pawn. To draw, all White has to do is shift his king back and forth between these two squares, e1 and e2{R}{C}{S:d1e1}{W:10_01Ig}. If ever Black's king moves to {S:d4d3}{W:10_01Ih}d3, White draws by moving his king to {S:e1d1}{W:10_01Ii}d1, taking the opposition. If Black instead has the chance to maneuver his king to {B:40/4pk2/8/4K3}{W:10_01Ij}f3, White keeps the draw by moving his king to {S:e1f1}{W:10_01Ik}f1. In both cases, White's king holds the draw by opposing the Black king as it comes to the attacker's 6th rank. In other words, White draws by "taking the opposition.";
1. Kd1-e1;{B:40/3kp3/8/3K4}{S:d1e1}{W:10_01C}Correct. If Black goes second, White will have to step to the side, 1. Kd1-e1, and the Black pawn can advance to the seventh rank without giving check {S:e3e2}{W:10_01Ca}(1... e3-e2). This will "squeeze" White's king off the home rank {S:e1f2}{W:10_01Cb}(2. Ke1-f2). Black will counter by moving his king ahead {S:d3d2}{W:10_01Cc}(2... Kd3-d2), which takes control of the promotion square and insures the making of a new queen on the next turn. It turns out that neither player wants to move in the given position. If Black goes first, he draws, and Black doesn't want to draw because he has the pawn. And if White goes first, he loses, and nobody wants to lose. A situation where neither player wants to move is called a mutual "zugzwang". Here it comes down to "the opposition." The opposition is a term referring to the relationship between the two kings. If you "have the opposition," it essentially means that you have the advantage, and that your king is in a position to exploit what the other king does. Why? Because you move second. Therefore you can wait and see what's best based on what the other side has done.}]

2.
[{B:6k1/8/4P3/6K1/32}{QB:2. Where should White move his king?{W:10_02}{A:Wg5f6}{H1:f6}{W:10_02a}{A:Wg5g6}{H1:g6}{W:10_02b};1. Kg5-f6;{B:6k1/8/4P3/6K1/32}{S:g5f6}{W:10_02I}Incorrect. Moving in this way (1. Kg5-f6) is quite natural, wanting to head toward the promotion square as soon as possible. But here it backfires, for it allows Black to "take the opposition" by moving the king to f8 {S:g8f8}{W:10_02Ia}(1... Kg8-f8). This draws, for if White advances the pawn to the 7th rank {S:e6e7}{W:10_02Ib}(2. e6-e7+), it's check. According to the rule, checking on the 7th rank with the pawn shouldn't win. The push gets nowhere after Black's king slides over to e8 {S:f8e8}{W:10_02Ic}(2... Kf8-e8), drawing next move by stalemate {A:Wf6e6}{N1:e6}{W:10_02Id}(3. Kf6-e6) or insufficient mating material (say {R}{C}{S:f6f5}{W:10_02Ie}3. Kf6-f5 {S:e8e7}{W:10_02If}Ke8xe7). And suppose White doesn't give a check on the second move. Let's assume he moves his king somewhere instead, say {B:5k2/8/4PK2/40}{S:f6e5}{W:10_02Ig}2. Kf6-e5. Black will then draw by shuttling his king between {S:f8e8}{N1:e7e8}{W:10_02Ih}e7 and e8, waiting for White's king to move up to its 6th rank, to either {A:We5d6}{A:We5f6}{N1:d6f6}{W:10_02Ii}d6 or f6. At this point Black draws by taking the opposition. He will move his king to {R}{C}{A:Be8d8}{W:10_02Ij}d8, when White's king is on {R}{S:e5d6}{W:10_02Ik}d6, or to {A:Be8f8}{W:10_02Il}f8, when White's king is on {S:d6f6}{W:10_02Im}f6.;
1. Kg5-g6;{B:6k1/8/4P3/6K1/32}{S:g5g6}{W:10_02C}Correct. Invading on king-knight-six (1. Kg5-g6) is the winning way, for it gives White the opposition. Black's best response is to move the king over to f8 {S:g8f8}{W:10_02Ca}(1... Kg8-f8), whereupon White's king also moves over {S:g6f6}{W:10_02Cb}(2. Kg6-f6), "maintaining the opposition" and insuring that the pawn will advance to the 7th rank without giving check. After {S:f8e8}{W:10_02Cc}2... Kf8-e8, White pushes the pawn {S:e6e7}{W:10_02Cd}(3. e6-e7), it's not check, and Black's king is squeezed off the back rank. Black could resign here, for moving the king to d7 {S:e8d7}{W:10_02Ce}(3... Ke8-d7) is followed by the incursion of White's king to f7 {S:f6f7}{W:10_02Cf}(4. Kf6-f7), with the pawn promoting {S:e7e8}{P:WQe8}{W:10_02Cg}(5. e8/Q) next move.}]

3.
[{B:8/3k4/8/2K5/3P4/24}{QB:3. Should White move his king or pawn?{W:10_03}{A:Wc5d5}{H1:d5}{W:10_03a}{A:Wd4d5}{W:10_03b};1. Kc5-d5;
{B:8/3k4/8/2K5/3P4/24}{S:c5d5}{W:10_03C}Correct. White's veracious strategy is to move the king (1. Kc5-d5), seizing the "direct opposition." Black's king will then have to give ground, to the right or left. If Black plays his king to c7 {S:d7c7}{W:10_03Ca}(1... Kd7-c7), White's king turns up the board to e6 {S:d5e6}{W:10_03Cb}(2. Kd5-e6). And if Black's monarch instead plays to e7 {B:8/3k4/8/3K4/3P4/24}{S:d7e7}{W:10_03Cc} (1... Kd7-e7), White's king has a "turning maneuver" up to c6 {S:d5c6}{W:10_03Cd}(2. Kd5-c6). In both instances, the White king has gotten to its 6th rank, ahead of its pawn, which is the general method of winning. A sample variation might go, {B:8/3k4/8/2K5/3P4/24}{S:c5d5}{W:10_03Ce}1. Kc5-d5 {S:d7c7}{W:10_03Cf}Kd7-c7  {S:d5e6}{W:10_03Cg}2. Kd5-e6 {S:c7d8}{W:10_03Ch}Kc7-d8  {S:d4d5}{W:10_03Ci}3. d4-d5 {S:d8e8}{W:10_03Cj}Kd8-e8 (taking a meaningless opposition, which can't be maintained) {S:d5d6}{W:10_03Ck}4. d5-d6, giving White a meaningful opposition, with the pawn on its 6th rank. Black gets squeezed out after {S:e8d8}{W:10_03Cl}4... Ke8-d8  {S:d6d7}{W:10_03Cm}5. d6-d7, and White makes a queen in two moves {S:d8c7}{W:10_03Cn}(5... Kd8-c7  {S:e6e7}{W:10_03Co}6. Ke6-e7 {S:c7c6}{W:10_03Cp}Kc7-c6  {S:d7d8}{P:WQd8}{W:10_03Cq}7. d7-d8/Q).;
1. d4-d5;{B:8/3k4/8/2K5/3P4/24}{S:d4d5}{W:10_03I}Incorrect. Pushing the pawn, 1. d4-d5?, is a mistake. It enables Black to steal the opposition meaningfully by {S:d7c7}{W:10_03Ia}1... Kd7-c7, and White has no way to regain it, assuming best play on the part of both combatants. (In all situations, we should assume that the opponent will play the best moves, because even if he's inexperienced he might play correctly by accident. Chessplayers don't gamble with the future unless the situation dictates it -- for example, they're hopelessly lost, so they have nothing to lose.) Let's look at a concrete variation.  After 1. d4-d5? Kd7-c7  {S:d5d6}{W:10_03Ib}2. d5-d6+ {S:c7d7}{W:10_03Ic}Kc7-d7 {S:c5d5}{W:10_03Id}3. Kc5-d5, Black holds the draw by retreating back to d8 {S:d7d8}{W:10_03Ie}(3... Kd7-d8), waiting for White's king to come to its 6th rank. At this point, Black will hold by taking the opposition. That is, he will answer {S:d5c6}{W:10_03If}4. Kd5-c6 by {S:d8c8}{W:10_03Ig} 4... Kd8-c8, or {B:3k4/8/3P4/3K4/32}{S:d5e6}{W:10_03Ih}4. Kd5-e6 by {S:d8e8}{W:10_03Ii}4... Kd8-e8, when White cannot advance the pawn to its 7th rank  without giving check. So the game is drawn.}]

4.
[{F:B}{B:6k1/24/4PK2/24}{QB:4. To draw the game, should Black move his king to f7 or f8?{W:10_04}{A:Bg8f7}{H1:f7}{W:10_04a}{A:Bg8f8}{H1:f8}{W:10_04b};1... Kg8-f7;{F:B}{B:6k1/24/4PK2/24}{S:g8f7}{W:10_04I}Incorrect. Moving the king to f7 (1... Kg8-f7), seems to be more aggressive, but it actually puts the king in a hole, for White garners the direct opposition by {S:f4f5}{W:10_04Ia}2. Kf4-f5. With precise play, the White king will be able to reach its 6th rank ahead of its pawn. For example, if Black continues {S:f7e7}{W:10_04Ib}2... Kf7-e7, White maintains the opposition with {S:f5e5}{W:10_04Ic}3. Kf5-e5, and Black will have to give ground, shifting the king to either d7 {A:Be7d7}{N1:d7}{W:10_04Id}(3... Ke7-d7) or f7 {A:Be7f7}{N1:f7}{W:10_04Ie}(3... Ke7-f7). White then follows with a turning maneuver, placing his own king squarely on its 6th rank. This he does by answering {F:B}{B:8/4k3/8/4K3/4P3/24}{S:e7d7}{W:10_04If}3... Ke7-d7 with {S:e5f6}{W:10_04Ig}4. Ke5-f6,  or {F:B}{B:8/4k3/8/4K3/4P3/24}{S:e7f7}{W:10_04Ih}3... Ke7-f7 with {S:e5d6}{W:10_04Ii} 4. Ke5-d6. From there it's a matter of utilizing the opposition so that the pawn advances to its 7th rank without giving check, which White can insure by force.;
1... Kg8-f8;{F:B}{B:6k1/24/4PK2/24}{S:g8f8}{W:10_04C}Correct. Black can escape with a draw by 1... Kg8-f8!, taking the "distant opposition," and waiting for White to commit himself to a king placement. That is, if White now plays {S:f4f5}{W:10_04Ca}2. Kf4-f5, Black will maintain the opposition with {S:f8f7}{W:10_04Cb}2... Kf8-f7. And if White instead plays {F:B}{B:5k2/24/4PK2/24}{S:f4e5}{W:10_04Cc}2. Kf4-e5, then Black keeps the opposition with {S:f8e7}{W:10_04Cd}2... Kf8-e7. In neither case can White make headway to regain the opposition. Black's opposition is meaningful and the game is drawn. A sample conclusion might go, {F:B}{B:6k1/24/4PK2/24}{S:g8f8}{W:10_04Ce}1... Kg8-f8  {S:f4e5}{W:10_04Cf}2. Kf4-e5 {S:f8e7}{W:10_04Cg}Kf8-e7 {S:e5d5}{W:10_04Ch}3. Ke5-d5 {S:e7d7}{W:10_04Ci}Ke7-d7 {S:e4e5}{W:10_04Cj}4. e4-e5 {S:d7e7}{W:10_04Ck}Kd7-e7 (note that his own pawn prevents White from taking the opposition by occupying e5, which is the square needed by the White king) {S:e5e6}{W:10_04Cl}5. e5-e6 (a bad omen for White, because the pawn has preceded its king to its 6th rank) {S:e7e8}{W:10_04Cm}5... Ke7-e8  {S:d5d6}{W:10_04Cn}6. Kd5-d6 {S:e8d8}{W:10_04Co}Ke8-d8 (taking the critical opposition as soon as White's king reaches its 6th rank) {S:e6e7}{W:10_04Cp}7. e6-e7+ (a check on the 7th rank, which is another bad sign for White) {S:d8e8}{W:10_04Cq}7... Kd8-e8 {S:d6e6}{W:10_04Cr}8. Kd6-e6, stalemate. The distant opposition is another expression of the oppositional relationship. As a general rule, when kings inhabit the same line (the same rank, file, or diagonal), they stand in opposition if two things are true, if both kings occupy squares of the same color, and if they are separated by an odd number of squares along the line of occupation. Thus, the kings stand in opposition when White's king is on g2 and Black's king is on a8, but not when White's king is on g2 and Black's king is on b7. When, as in the latter instance, the kings don't already stand in opposition, whoever moves can usually take the opposition. So with White's king on g2 and Black's on b7, Black to play can take the opposition by moving his king to {F:B}{B:8/1k6/32/6K1/8}{A:Bb7c6}{A:Bb7a8}{N1:c6a8}{W:10_04Cs}c6 or a8. Meanwhile, White to play can take the opposition by moving his king to either {R}{C}{A:Wg2f3}{A:Wg2h1}{N1:f3h1}{W:10_04Ct}f3 or h1.}]

5.
[{F:B}{B:16/1K6/p1p5/P1P5/1k6/16}{QB:5. Should Black take a pawn or simply move his king?{W:10_05}{A:Bb3c4}{H1:c4}{W:10_05a}{A:Bb3b4}{H1:b4}{W:10_05b};
1... Kb3xc4;{F:B}{B:16/1K6/p1p5/P1P5/1k6/16}{S:b3c4}{W:10_05I}Incorrect. Taking either pawn leads to a draw. Let's say Black takes the c-pawn, 1... Kb3xc4. White will counter by taking Black's a-pawn, {S:b6a5}{W:10_05Ia}2. Kb6xa5. Then it becomes a race to see who will queen first, and even then it might not matter. The game is probably still drawn as long as both players queen on the same move and neither one is hindered by virtue of being in check. (There are many entertaining twists on this scenario, as in the concluding scene from the film Searching for Bobby Fischer.) So after 1... Kb3xc4  2. Kb6xa5, the position should be drawn after {S:c4b3}{W:10_05Ib}2... Kc4-b3  {S:a5b6}{W:10_05Ic}3. Ka5-b6 {S:c5c4}{W:10_05Id}c5-c4. Now it doesn't help on move three to take White's a-pawn, {S:c4c5}{S:b3a4}{W:10_05Ie}3... Kb3xa4, for White then takes Black's c-pawn, {S:b6c5}{W:10_05If}4. Kb6xc5, and the game is drawn because there's nothing left. The concluding moves after {F:B}{B:16/1K6/2p5/P7/1k6/16}{S:c5c4}{W:10_05Ig}3... c5-c4 are likely to be {S:a4a5}{S:a4a5}{W:10_05Ih}4. a4-a5 {S:c4c3}{W:10_05Ii}c4-c3  {S:a5a6}{W:10_05Ik}5. a5-a6 {S:c3c2}{W:10_05Il}c3-c2 {S:a6a7} {W:10_05Im}6. a6-a7 {S:c2c1}{P:BQc1}{W:10_05In}c2-c1/Q  {S:a7a8}{P:WQa8}{W:10_05Io}7.a7-a8/Q, when both players have added a queen. Although Black can be the first to start giving checks, he can't do any real damage with them. The position is drawn. A similar draw would also result from a different initial capture, if Black instead were to take the a-pawn {F:B}{B:16/1K6/p1p5/P1P5/1k6/16}{S:b3a4}{W:10_05Ip}(1... Kb3xa4). This too would lead to comparably harmless promotions for both sides, where neither player comes out on top.;
1... Kb3-b4;{F:B}{B:16/1K6/p1p5/P1P5/1k6/16}{S:b3b4}{W:10_05C}Correct. Instead of trading pawns, Back can prevent White from getting anything by delaying the capture in favor of taking the opposition, {W:10_05Ca}1... Kb3-b4!. No matter which way the White king now goes, Black can take a pawn while keeping his own pawns protected. The result is that Black gets both White pawns, and White gets nothing. If White replies to 1... Kb3-b4! by moving his king to the c-file {S:b6c6}{W:10_05Cb}(2. Kb6-c6), Black takes the c-pawn {S:b4c4}{W:10_05Cc}(2... Kb4xc4), and White is fleeced. And if White instead moves his king to the a-file {F:B}{B:16/1K6/p1p5/PkP5/24}{S:b6a6}{W:10_05Cd}(2. Kb6-a6), then the a-pawn is filched {S:b4a4}{W:10_05Ce}(2... Kb4xa4), and again White gets zilch. Black will soon be on his way to making a new queen, and White is as helpless to stop it as a high-schooler trying to guard Michael Jordan.}]

6.
[{F:W}{B:8/kP6/2K5/1P6/32}{QB:6. Which pawn move should White make?{W:10_06}{A:Wb5b6}{H1:b6}{W:10_06a}{A:Wb7b8}{H1:b8}{W:10_06b};1. b5-b6+;
{B:8/kP6/2K5/1P6/32}{S:b5b6}{W:10_06I}Incorrect. Pushing the b5-pawn (1. b5-b6+) is a clear mistake. Black will retreat the king to b8 {S:a7b8}{W:10_06Ia}(1... Ka7-b8), and White must abandon the b7-pawn, say {S:c6c5}{W:10_06Ib}2. Kc6-c5, for he has no place to put the king that keeps pawn protected. After the pawn is taken {S:b8b7}{W:10_06Ic}(2... Kb8xb7), Black's king is in perfect shape to control the draw. It plays back and forth between {N1:b7b8}{W:10_06Id}b7 and b8, waiting for White's king to come up to the 6th rank. Whenever this happens, Black will be armed to take the opposition, while White is unable to advance the pawn without giving check. So the position is drawn.;
1. b7-b8/Q+;{B:8/kP6/2K5/1P6/32}{S:b7b8}{P:WQb8}{W:10_06C}Correct. It turns out that two pawns are too much. If White wants to win he needs to ditch one of them, the front one, by advancing it to the last row (1. b7-b8/Q+). Note that moving the White king up one square {A:Wc6c7}{W:10_06Ca}(1. Kc6-c7) doesn't help, for this is stalemate. Back to the prudent sacrifice, 1. b7-b8/Q+. After Black takes the queen {R}{S:a7b8}{W:10_06Cb}(1... Ka7xb8), White doesn't have to worry about giving stalemate any longer, because now he has much more room for maneuvering. It's a palpable case of less being more. The win is now simple. White takes the opposition, {S:c6b6}{W:10_06Cc}2. Kc6-b6, and regardless whether Black moves his king to the left or right, White wins by moving his king up one square in the other direction. That is, in response to Black's king moving to the corner {S:b8a8}{W:10_06Cd}(2... Kb8-a8), White clears a path for the pawn by advancing his king to c7 {S:b6c7}{W:10_06Ce}(3. Kb6-c7). Meanwhile, if Black's king goes the other way {B:1k7/8/1K6/1P6/32}{S:b8c8}{W:10_06Cf}(2... Kb8-c8),  White wins by reversing direction {S:b6a7}{W:10_06Cg}(3. Kb6-a7), and again the pawn is unstoppable.}]

7.
[{F:B}{B:k7/8/1p6/3K4/1P6/24}{QB:7. Should Black move his pawn or king?{W:10_07}{A:Bb6b5}{H1:b5}{W:10_07a}{A:Ba8b7}{H1:b7}{W:10_07b};1... b6-b5;
{F:B}{B:k7/8/1p6/3K4/1P6/24}{S:b6b5}{W:10_07C}Correct. Superficially, advancing (1... b6-b5) appears absurd, inasmuch as White can gain the pawn perforce. White acquires it by moving his king to either {A:Wd5c5}{A:Wd5c6}{N1:c5c6}{W:10_07Ca}c5 or c6, and Black can do nothing to save it. But this doesn't matter, for after {R}{C}{S:d5c6}{W:10_07Cb}2. Kd5-c6 {S:a8b8}{W:10_07Cc}Ka8-b8  {S:c6b5}{W:10_07Cd}3. Kc6xb5, White indeed has won a pawn, but Black gains a meaningful opposition with {S:b8b7}{W:10_07Ce}3... Kb8-b7. This promethean defense will prevent White's king from ever getting to its 6th rank ahead of its pawn. For instance, the game would remain drawn after {S:b5c5}{W:10_07Cf}4. Kb5-c5 {S:b7c7}{W:10_07Cg}Kb7-c7 {S:b4b5}{W:10_07Ch}5. b4-b5. This last move gets White the opposition, but it's a meaningless opposition because it can't be maintained. Black proves this by continuing, {S:c7b7}{W:10_07Ci}5... Kc7-b7, when White is unable to take the opposition because his own pawn blocks b5. So White advances it, {S:b5b6}{W:10_07Cj}6. b5-b6, but this means that the pawn precedes its own king to the 6th rank, which is a no-no. Black therefore withdraws his king {S:b7b8}{W:10_07Ck}(Kb7-b8), making sure to stay on the same file as the pawn, so that after, {S:c5c6}{W:10_07Cl}7. Kc5-c6, Black can take a meaningful opposition by {S:b8c8}{W:10_07Cm}7... Kb8-c8. No progress can be made. If White pushes his pawn {S:b6b7}{W:10_07Cn}(8. b6-b7+), it's with check on the 7th rank, and this too doesn't work. The game would then end after {S:c8b8}{W:10_07Co}8... Kc8-b8, for {S:c6b6}{W:10_07Cp}9. Kc6-b6 is stalemate. Clearly, in king and pawn endings, material isn't everything. Surely the quality of the material also matters, as does the position of the two kings. If one is especially dominant, it may be able to compensate for an overall deficit in force by deterring the opponent's king from doing its job.;
1... Ka8-b7;{F:B}{B:k7/8/1p6/3K4/1P6/24}{S:a8b7}{W:10_07I}Incorrect. Actively using the king tends to be an apropos approach, but here, 1... Ka8-b7, leads to defeat. True, Black doesn't drop the pawn for a few moves, but he does lose it for sure, beginning with the stultifying advance, {S:b4b5}{W:10_07Ia}2. b4-b5!. Now Black is going to run out of maneuvering room, even after, {S:b7c7}{W:10_07Ib}2... Kb7-c7. White's king merely enters on e6, dances it's way over to c6 or c7, and the pawn falls when Black's king is denied space and places to go. A possible winning variation might be, {S:d5e6}{W:10_07Ic}3. Kd5-e6 {S:c7c8}{W:10_07Id}Kc7-c8 (taking a meaningless diagonal opposition) {S:e6d6}{W:10_07Ie}4. Ke6-d6 {S:c8b7}{W:10_07If}Kc8-b7  {S:d6d7}{W:10_07Ig}5. Kd6-d7 (the dance of death continues) {S:b7b8}{W:10_07Ih}5... Kb7-b8 {S:d7c6}{W:10_07Ii}6. Kd7-c6 {S:b8a7}{W:10_07Ij}Kb8-a7, when after {S:c6c7}{W:10_07Ik}7. Kc6-c7, Black must cede the b-pawn to White's invasive king {S:a7a8}{W:10_07Il}(7... Ka7-a8  {S:c7b6}{W:10_07Im}8. Kc7xb6). The terminating moves might be, {S:a8b8}{W:10_07In}8... Ka8-b8 (taking the opposition, but a valueless one, for White's king is already on the 6th rank, ahead of its pawn, so the opposition can't be maintained) {S:b6a6}{W:10_07Io}9. Kb6-a6 {S:b8a8}{W:10_07Ip}Kb8-a8  {S:b5b6} {W:10_07Iq}10. b5-b6 {S:a8b8}{W:10_07Ir}Ka8-b8  {S:b6b7}{W:10_07Is}11. b6-b7, advancing the pawn to its 7th rank without giving check. This will squeeze Black's king off the back rank {S:b8c7}{W:10_07It}(11... Kb8-c7), and White's own king advances to its 7th rank {S:a6a7}{W:10_07Iu}(12. Ka6-a7), supporting the pawn's promotion on the very next move.}]

8.
[{F:B}{B:7k/8/7K/8/ppp5/8/PPP5/8}{QB:8. Which pawn should Black move?{W:10_08}{A:Bb4b3}{H1:b3}{W:10_08a}{A:Bc4c3}{H1:c3}{W:10_08b};the b-pawn;
{F:B}{B:7k/8/7K/8/ppp5/8/PPP5/8}{S:b4b3}{W:10_08C}Correct. Moving the b-pawn (1... b4-b3) creates a decisive breakthrough. No matter how White replies, Black is assured of sneaking a pawn past the enemy defenders to become a new queen. Let's say that White takes with the a-pawn {S:a2b3}{W:10_08Ca}(2. a2xb3). In this case, it's the a4-pawn that eventually promotes, but only after Black first offers another sacrifice, the c-pawn at c3 {S:c4c3}{W:10_08Cb}(2... c4-c3). This threatens to capture on b2. So White has no practical choice. He must take on c3 {S:b2c3}{W:10_08Cc}(3. b2xc3), just for self-defense, whereupon Black's a-pawn penetrates with {S:a4a3}{W:10_08Cd}3... a4-a3. It queens in two moves. Black wins in a similar way if on move two it's White's c-pawn that captures on b3 {F:B}{B:7k/8/7K/8/p1p5/1p6/PPP5/8}{S:c2b3}{W:10_08Ce}(2. c2xb3). In this instance, Black breaks through with his c-pawn by first sacrificing the a-pawn {S:a4a3}{W:10_08Cf}(2... a4-a3). White again has no viable choice. He must accept the offering {S:b2a3}{W:10_08Cg}(3. b2xa3), and now the c-pawn scurries toward the c1-promotion square {S:c4c3}{W:10_08Ch}(3... c4-c3), soon to emerge as a new queen.;
the c-pawn;{F:B}{B:7k/8/7K/8/ppp5/8/PPP5/8}{S:c4c3}{W:10_08I}Incorrect. Advancing the queen-bishop pawn (1... c4-c3) fails to the direct exchange, {S:b2c3}{W:10_08Ia}2. b2xc3. After Black recaptures {S:b4c3}{W:10_08Ib}(2... b4xc3), White's king heads back toward the queenside {S:h6g6}{W:10_08Ic}(3. Kh6-g6), and Black stands to lose both his remaining pawns. If it were White's move to start with, he could prevent the breakthrough combination by actually obstructing the advance of Black's middle pawn. This he could do by {B:7k/8/7K/8/ppp5/8/PPP5/8}{S:b2b3}{W:10_08Id}1. b2-b3. After the ensuing exchanges {S:a4b3}{W:10_08Ie}(1... a4xb3 {S:a2b3}{W:10_08If}2. a2xb3 {S:c4b3}{W:10_08Ig}c4xb3  {S:c2b3}{W:10_08Ih}3. c2xb3), White's king can get back to win the then solitary Black pawn, but Black's own king will be able to gain a meaningful opposition afterward to draw. In other words, when White's king captures on b4, Black's king will be able to move to b6, taking the direct opposition and halting further progress. The variation might go, {S:h8g8}{W:10_08Ii}3... Kh8-g8  {S:h6g6}{W:10_08Ij}4. Kh6-g6 {S:g8f8}{W:10_08Ik}Kg8-f8 {S:g6f6}{W:10_08Il}5. Kg6-f6 {S:f8e8}{W:10_08Im}Kf8-e8 {S:f6e6}{W:10_08In}6. Kf6-e6 {S:e8d8}{W:10_08Io}Ke8-d8 {S:e6d6}{W:10_08Ip}7. Ke6-d6 {S:d8c8}{W:10_08Iq}Kd8-c8 {S:d6c5}{W:10_08Ir}8. Kd6-c5 {S:c8c7}{W:10_08Is}Kc8-c7 {S:c5b4}{W:10_08It}9. Kc5xb4 {S:c7b6}{W:10_08Iu}Kc7-b6, gaining the direct opposition, with a draw in hand. A sample conclusion, without comment, is, {S:b4c4}{W:10_08Iv}10. Kb4-c4 {S:b6c6}{W:10_08Iw}Kb6-c6 {S:b3b4}{W:10_08Ix}11. b3-b4 {S:c6b6}{W:10_08Iy}Kc6-b6 {S:b4b5}{W:10_08Iz}12. b4-b5 {S:b6b7}{W:10_08Iza}Kb6-b7 {S:c4c5}{W:10_08Izb}13. Kc4-c5 {S:b7c7}{W:10_08Izc}Kb7-c7 {S:b5b6}{W:10_08Izd}14. b5-b6+ {S:c7b7}{W:10_08Ize}Kc7-b7 {S:c5b5}{W:10_08Izf}15. Kc5-b5 {S:b7b8}{W:10_08Izg}Kb7-b8 {S:b5a6}{W:10_08Izh}16. Kb5-a6 {S:b8a8}{W:10_08Izi}Kb8-a8 {S:b6b7}{W:10_08Izj}17. b6-b7+ {S:a8b8}{W:10_08Izk}Ka8-b8 {S:a6b6}{W:10_08Izl}18. Ka6-b6, stalemate.}]

9.
[{F:B}{B:16/2p5/p7/2kP4/2P5/2K5/8}{QB:9. Which pawn should Black push?{W:10_09}{A:Ba5a4}{H1:a4}{W:10_09a}{A:Bc6c5}{H1:c5}{W:10_09b};the a-pawn;
{F:B}{B:16/2p5/p7/2kP4/2P5/2K5/8}{S:a5a4}{W:10_09C}Correct. Black has what's called the "outside passed pawn," which here is represented by the a-pawn. In general, such a pawn is "outside" the main theatre of action, and often can be used as a decoy to lure away the opposing king. With the opposing king thus removed, the friendly king can move in on the suddenly vulnerable targets, possibly cleaning up the remaining pawns without resistance. After 1... a5-a4, White has nothing better than {S:c2b2}{W:10_09Ca}2. Kc2-b2, whereupon Black can ditch the a-pawn, {A:Ba4a3}{W:10_09Cb}2... a4-a3+, or even just invade with his king, {R}{A:Bc4d3}{W:10_09Cc}2... Kc4-d3, either way soon winning the two White pawns and insuring the promotion of his remaining c-pawn.;
the c-pawn;{F:B}{B:16/2p5/p7/2kP4/2P5/2K5/8}{S:c6c5}{W:10_09I}Incorrect. Moving the c-pawn (1... c6-c5?) is a blunder. Why should Black offer to trade c-pawn for d-pawn when he can win the d-pawn by force? (As a rule, you don't trade what you might be able to win.) So the defender simply exchanges pawns {S:d4c5}{W:10_09Ia}(2. d4xc5 {S:c4c5}{W:10_09Ib}Kc4xc5), and after {S:c2b3}{W:10_09Ic}3. Kc2-b3, White will be able to survive without much hassle. In fact, at this point, White doesn't even have to defend his c-pawn. If Black should actually win it, he'd be left with the a-pawn alone, and there's no way that the a-pawn can be forced through to queen with White's king already in front of it. There'd be no way to force the White king out of the corner. Try it. You'll see what I mean. Just keep shuttling your king between a1 and b1. Eventually Black will be constrained to advance his a-pawn to its 7th rank, and stalemate ensues.}]

10.
[{F:B}{B:24/7p/5kpP/8/7K/8}{QB:10. Should Black move his king or pawn?{W:10_10}{A:Bf4f3}{H1:f3}{W:10_10a}{A:Bg4g3}{H1:g3}{W:10_10b};1... Kf4-f3;
{F:B}{B:24/7p/5kpP/8/7K/8}{S:f4f3}{W:10_10C}Correct. Invading with the king (1... Kf4-f3) gains the White h-pawn in a couple of moves. White will have to give ground {S:h2g1}{W:10_10Ca}(say 2. Kh2-g1), and Black then shifts over to attack White's lonesome pawn {S:f3g3}{W:10_10Cb}(2... Kf3-g3), which can't be protected. Next turn, Black usurps the pawn {S:g3h4}{W:10_10Cc}(3... Kg3xh4), with promotion soon to follow. A sample variation is, {F:B}{B:24/7p/6pP/6k1/8/6K1}{S:g1h1}{W:10_10Cd}3. Kg1-h1 {S:g3h4}{W:10_10Ce}Kg3xh4 {S:h1h2}{W:10_10Cf}4. Kh1-h2 (taking a meaningless opposition) {S:g4g3}{W:10_10Cg}4... g4-g3+  {S:h2g2}{W:10_10Ch}5. Kh2-g2 {S:h4g4}{W:10_10Ci}Kh4-g4  {S:g2g1}{W:10_10Cj}6. Kg2-g1 {S:g4f3}{W:10_10Ck}Kg4-f3 {S:g1f1}{W:10_10Cl}7. Kg1-f1 {S:g3g2}{W:10_10Cm}g3-g2+ (this check is okay because of the extra pawn on the h-file, which enables Black to avert stalemate) {S:f1g1}{W:10_10Cn}8. Kf1-g1 {S:h5h4}{W:10_10Co}h5-h4 {S:g1h2}{W:10_10Cp}9. Kg1-h2 {S:f3f2}{W:10_10Cq}Kf3-f2  {S:h2h3}{W:10_10Cr}10. Kh2-h3 {S:g2g1}{P:BQg1}{W:10_10Cs}g2-g1/Q {S:h3h4}{W:10_10Ct}11. Kh3xh4 {S:g1g6}{W:10_10Cu}Qg1-g6 (chasing the White king back the other way) {S:h4h3}{W:10_10Cv}12. Kh4-h3 {A:Bg6h5}{N1:h5}{W:10_10Cw}Qg6-h5# (or {R}{C}{S:g6g3}{W:10_10Cx}12... Qg6-g3#).;
1... g4-g3+;{F:B}{B:24/7p/5kpP/8/7K/8}{S:g4g3}{W:10_10I}Incorrect. Pushing the pawn (1... g4-g3+?) may look delicious, but it's actually quite unsavory. After White hides his king at h3 {S:h2h3}{W:10_10Ia}(2. Kh2-h3), Black must either abandon his g-pawn, which leads to a drawn game (because only rook-pawns would remain), or keep the g-pawn guarded by {S:f4f3}{W:10_10Ib} 2... Kf4-f3, which is stalemate on any continent.}]

11.
[{F:W}{B:5k2/32/2P5/8/3K4}{QB:11. Where should White move his king?{W:10_11}{A:Wd1d2}{H1:d2}{W:10_11a}{A:Wd1c2}{H1:c2}{W:10_11b};to d2;
{B:5k2/32/2P5/8/3K4}{S:d1d2}{W:10_11I}Incorrect. The natural move is 1. Kd1-d2, but it's also the wrong move. Black will be able to get his king over just in time to draw. For example, after {S:f8e7}{W:10_11Ia}1...Kf8-e7 {S:d2d3}{W:10_11Ib}2. Kd2-d3, Black retains his dignity with {S:e7d7}{W:10_11Ic}2... Ke7-d7, taking the distant opposition, and waiting for White's king to commit itself to c4 or d4. If the king goes to c4 {S:d3c4}{W:10_11Id}(3. Kd3-c4), Black maintains the opposition by moving his king to c6 {S:d7c6}{W:10_11Ie}(3... Kd7-c6). And if the White king instead goes to d4 {B:8/3k4/24/2PK4/16}{S:d3d4}{W:10_11If}(3. Kd3-d4), Black keeps the opposition by going to d6 {S:d7d6}{W:10_11Ig}(3... Kd7-d6). In each case, Black holds the opposition and guarantees a draw.;
to c2;{B:5k2/32/2P5/8/3K4}{S:d1c2}{W:10_11C}Correct. The right move is 1. Kd1-c2, heading for the "outside critical square" at b5. In king and pawn endings, a square is "critical" if its occupation by the superior side's king creates a winning position. (This doesn't imply that the position isn't winning before the square is occupied by the dominant side's king. It simply means that further progress can't be made until such an occupation is realized.) Most passed pawns are associated with a set of "critical squares." The critical squares tend to be two ranks ahead of the passed pawn to which they correspond. So, with a White pawn on c3, the critical squares are {N1:b5c5d5}{W:10_11Ca}b5, c5, and d5. If White's king can reach any of these three squares, White will be able to force a win. If Black's king can stop White from doing this (from reaching b5, c5, or d5 with a White pawn on c3), the game would be drawn. Here, the move 1. Kd1-c2 enables White's king to get to the outside critical square b5 by force. The game might then continue, {C}{S:f8e7}{W:10_11Cb}1... Kf8-e7  {S:c2b3}{W:10_11Cc}2. Kc2-b3 {S:e7d6}{W:10_11Cd}Ke7-d6  {S:b3b4}{W:10_11Ce}3. Kb3-b4, threatening to move the king to b5. The only way Black can try to stop this beachhead is by moving his king over to c6 {S:d6c6}{W:10_11Cf}(3... Kd6-c6), which actually guards b5, preventing its immediate occupation by the White king. Nonetheless, White can then take the direct opposition by {S:b4c4}{W:10_11Cg}4. Kb4-c4, with a position that can be won by force. Black's king will have to step to the side {N1:b6d6}{W:10_11Ch}(to b6 or d6), and White's king advances to a critical square {N1:d5b5}{W:10_11Ci}to either d5 or b5, depending which way Black has gone). From there, White wins by carefully escorting his pawn to the promotion square.}]

12.
[{F:B}{B:8/p7/P7/16/6K1/8/6k1}{QB:12. Should Black move his king toward the corner or toward the center?{W:10_12}{A:Wg1h1}{H1:h1}{W:10_12a}{A:Wg1f1}{H1:f1}{W:10_12b};1... Kg1-h1;{B:8/p7/P7/16/6K1/8/6k1}{S:g1h1}{W:10_12C}Correct. The ridiculous-looking move, 1... Kg1-h1, is the best move. Although it seems to be moving the king away from the action, it's actually bringing it closer to the critical line of retreat, the {N1:b8c7d6e5f4g3h2}{W:10_12Ca}b8-h2 diagonal. By using this diagonal, Black's king is able to occupy c7 immediately after White's king captures the Black pawn on a7. This will soon produce a draw. For example, after 1... Kg1-h1 {C}{S:g3f3}{W:10_12Cb}2. Kg3-f3, Black's king can chase White's king along the proper channel by moving to {S:h1h2}{W:10_12Cc}h2. There could follow {S:f3e4}{W:10_12Cd} 3. Kf3-e4 {S:h2g3}{W:10_12Ce}Kh2-g3 {S:e4d5}{W:10_12Cf}4. Ke4-d5 {S:g3f4}{W:10_12Cg}Kg3-f4 {S:d5c6}{W:10_12Ch}5. Kd5-c6 {S:f4e5}{W:10_12Ci}Kf4-e5 {S:c6b7}{W:10_12Cj}6. Kc6-b7 {S:e5d6}{W:10_12Ck}Ke5-d6 {S:b7a7}{W:10_12Cl}7.  Kb7xa7, when Black traps the White king by {S:d6c7}{W:10_12Cm}7... Kd6-c7. And if White deigns to continue by occupying the corner, {S:a7a8}{W:10_12Cn}8. Ka7-a8, the game is likely to end with Black stalemating White, {S:c7b6}{W:10_12Co}8... Kc7-b6  {S:a6a7}{W:10_12Cp}9. a6-a7 {S:b6c7}{W:10_12Cq}Kb6-c7.;
1... Kg1-f1;{B:8/p7/P7/16/6K1/8/6k1}{S:g1f1}{W:10_12I}Incorrect. Moving the king toward the center (1... Kg1-f1) loses, starting with the reply, {S:g3f3}{W:10_12Ia}2. Kg3-f3. If Black then tries to get on the right line {N1:b8c7d6e5f4g3h2}{W:10_12Ib}(the b8-h2 diagonal) by going back the other way, {S:f1g1}{W:10_12Ic}2... Kf1-g1, White uses his extra tempo to gain the victory, {C}{S:f3e4}{W:10_12Id}3. Kf3-e4 {S:g1f2}{W:10_12Ie}Kg1-f2 (playing the Black king to h2 is no longer germane -- try it and see) {S:e4d5}{W:10_12If}4. Ke4-d5 {S:f2e3}{W:10_12Ig}Kf2-e3 {S:d5c6}{W:10_12Ih}5. Kd5-c6 {S:e3d4}{W:10_12Ii}Ke3-d4  {S:c6b7}{W:10_12Ij}6. Kc6-b7 {S:d4c5}{W:10_12Ik}Kd4-c5  {S:b7a7}{W:10_12Il}7. Kb7xa7 {S:c5c6}{W:10_12Im}Kc5-c6  {S:a7b8}{W:10_12In}8. Ka7-b8, and the pawn can't be stopped. So this example represents another one of those strange chess cases, which seem to defy the rules. By moving further away {B:8/p7/P7/16/6K1/8/6k1}{S:g1h1}{W:10_12Io}(1... Kg1-h1), in some sense Black was actually moving closer -- that is, closer to the critical diagonal leading to the key defensive square c7. This example also shows the value of diagonal king moves, which can often do the seemingly impossible. Often, not always.}]

13.
[{F:W}{B:8/5p2/4p3/8/3P4/5k2/P7/5K2}{QB:13. Which pawn should White advance?{W:10_13}{A:Wa2a4}{H1:a4}{W:10_13a}{A:Wd4d5}{H1:d5}{W:10_13b};the a-pawn;
{B:8/5p2/4p3/8/3P4/5k2/P7/5K2}{S:a2a4}{W:10_13I}Incorrect. Pushing the a-pawn (1. a2-a4), the outside passed pawn, is naturally the idea to be considered first, for typically it would be the hardest pawn for the opposing king to catch. But it's easy to see that after the Black king starts its retreat along the critical {N1:a8b7c6d5e4f3g2h1}{W:10_13Ia}a8-h1 diagonal {C}{S:f3e4}{W:10_13Ib}(1... Kf3-e4), the a-pawn is going to be overtaken and won, {S:a4a5}{W:10_13Ic}2. a4-a5 {S:e4d5}{W:10_13Id}Ke4-d5  {S:a5a6}{W:10_13Ie}3. a5-a6 {S:d5c6}{W:10_13If}Kd5-c6 {S:a6a7}{W:10_13Ig}4. a6-a7 {S:c6b7}{W:10_13Ih}Kc6-b7, and indeed the pawn falls. Generally, there's a visual trick enabling you to tell if a passed pawn can be caught by the defending king. Draw a mental line from the square on which the pawn sits to the square of promotion. This imaginary line forms the side of a mentally constructed box of squares. If the defending king can move inside the box, it can catch the pawn. If the king can't do this, the pawn will queen. For example, with the White a-pawn on a5, the box contains 16 squares, {B:8/5p2/4p3/P7/3Pk3/16/5K2}{N1:a5a6a7a8b8c8d8d7d6d5c5b5}{W:10_13Ii}and runs from a5 to a8 to d8 to d5 to a5. If Black's king can enter the box at d5 (or d6,  d7,  d8, c5, or b5), the pawn becomes dead meat. From the starting position of our example, this very thing {S:e4d5}{W:10_13Ij}(2... Ke4-d5) is done on Black's second move.;
the d-pawn;{B:8/5p2/4p3/8/3P4/5k2/P7/5K2}{S:d4d5}{W:10_13C}Correct. White can prevent Black's king from utilizing the critical diagonal of retreat by sacrificing his d-pawn, 1. d4-d5!. Black must take the pawn, which creates a block at d5.{S:e6d5}{W:10_13Ca} This obstacle prevents Black's king from getting back to stop the pawn because the critical diagonal of retreat {N1:a8b7c6d5e4f3g2h1}{W:10_13Cb}(a8-h1) is now closed, {C}{S:a2a4}{W:10_13Cc}2. a2-a4 {S:f3e4}{W:10_13Cd}Kf3-e4  {S:a4a5}{W:10_13Ce}3. a4-a5, and now Black is unable to enter the square at d5, and the pawn queens by force. So after {B:8/5p2/8/3p4/P7/5k2/8/5K2}{W:10_13Cf} 2. a2-a4, the defender has nothing better than trying a counterattack, {S:d5d4}{W:10_13Cg}2... d5-d4. Black thereby hopes that after {S:a4a5}{W:10_13Ch}3. a4-a5 {S:d4d3}{W:10_13Ci}d4-d3, White will continue the pedestrian advance of his a-pawn {S:a5a6}{W:10_13Cj}4. a5-a6?), which permits Black to the turn the tables by {S:d3d2}{W:10_13Ck}4... d3-d2, queening and soon mating. But White doesn't have to fall for this stratagem, for he can answer Black's third move (3... d4-d3) by employing a little defense {B:8/5p2/8/P7/8/3p1k2/8/5K2}{S:f1e1}{W:10_13Cl}(4. Kf1-e1), and this stops the Black d-pawn in its tracks. On the next move, White's a-pawn can proceed merrily on its way {S:a5a6}{W:10_13Cm}(5. a5-a6).}]

14.
[{F:B}{B:24/1pK5/8/6P1/8/4k3}{QB:14. Should Black move his king toward the White pawn, or away from it?{W:10_14}{A:Be1f2}{H1:f2}{W:10_14a}{A:Be1d2}{H1:d2}{W:10_14b};1... Ke1-f2;{F:B}{B:24/1pK5/8/6P1/8/4k3}{S:e1f2}{W:10_14I}Incorrect. Black has no real chance to catch the pawn with a direct attack (1... Ke1-f2), for White just pushes ahead {S:g3g4}{W:10_14Ia}(2. g3-g4), and the pawn will queen for sure. A king is simply unable to overtake a pawn with a two-rank head start in a pawn race. In order to do this, there would have to be a tactical trick that gains time, and 1... Ke1-f2 doesn't do it.;
1... Ke1-d2;{F:B}{B:24/1pK5/8/6P1/8/4k3}{S:e1d2}{W:10_14C}Correct. Here's another chess paradox. By apparently veering away from the pawn (1... Ke1-d2), Black actually winds up moving closer to it. It comes down to this. Moving toward his own pawn enables Black to muster a time-gaining threat, which White can't ignore. White is forced to play a defensive move, and it's this tempo that salvages the draw. The analysis confirms it. After 1... Ke1-d2, White can try to win in either of two ways. He can take the Black pawn {S:c5b5}{W:10_14Ca}(2. Kc5xb5), though this permits Black to gain on the White pawn diagonally {S:d2e3}{W:10_14Cb}(2... Kd2-e3), leading to its capture in two moves {S:g3g4}{W:10_14Cc}(3. g3-g4 {S:e3f4} {W:10_14Cd}Ke3-f4 {S:g4g5}{W:10_14Ce}4. g4-g5 {S:f4g5}{W:10_14Cf}Kf4xg5). Or he can start the g-pawn on its way at once, {F:B}{B:24/1pK5/8/6P1/3k4/8}{S:g3g4}{W:10_14Cg} 2. g3-g4. To this, Black continues in his paradoxical manner, moving his king even further away with, {S:d2c3}{W:10_14Ch} 2... Kd2-c3. This threatens to protect his own pawn by pushing it to b4. Either both sides will now queen innocuously, as in the line {S:g4g5}{W:10_14Ci}3. g4-g5 {S:b5b4}{W:10_14Cj}b5-b4  {S:g5g6}{W:10_14Ck}4. g5-g6 {S:b4b3}{W:10_14Cl}b4-b3  {S:g6g7}{W:10_14Cm}5. g6-g7 {S:b3b2}{W:10_14Cn}b3-b2  {S:g7g8}{P:WQg8}{W:10_14Co}6. g7-g8/Q {S:b2b1}{P:BQb1}{W:10_14Cp}b2-b1/Q, which should end in a draw. Or White opts to take Black's pawn {F:B}{B:24/1pK5/6P1/2k5/16}{S:c5b5}{W:10_14Cq}(3. Kc5xb5), when Black can then catch up with the g-pawn by heading back, {S:c3d4}{W:10_14Cr}3... Kc3-d4  {S:g4g5}{W:10_14Cs}4. g4-g5 {S:d4e5}{W:10_14Ct}Kd4-e5 {S:g5g6}{W:10_14Cu}5. g5-g6 {S:e5f6}{W:10_14Cv}Ke5-f6, and the pawn goes next move.}]

15.
[{F:W}{B:2r3k1/5pp1/p6p/1p2p3/3pP3/3P4/PP3PPP/4K2R}{QB:15. Should White castle or move his king to d2?{W:10_15}{A:We1g1}{A:Wh1f1}{H1:f1g1}{W:10_15a}{A:We1d2}{H1:d2}{W:10_15b};1. 0-0;
{B:2r3k1/5pp1/p6p/1p2p3/3pP3/3P4/PP3PPP/4K2R}{S:e1g1}{S:h1f1}{W:10_15I}Incorrect. The principled move is to castle, 1. 0-0, but this permits a decisive intrusion to the 7th rank, {S:c8c2}{W:10_15Ia}1... Rc8-c2, when it becomes quite difficult for White to hold onto his pawns. For example, if {S:f1b1}{W:10_15Ib}2. Rf1-b1, to defend the b-pawn, Black pilfers the d-pawn by {S:c2d2}{W:10_15Ic}2... Rc2-d2. Sometimes castling isn't the safest move at all. Sometimes it removes the king from an area that requires its support. Take away the king, and the region could become defenseless.;
1. Ke1-d2;{B:2r3k1/5pp1/p6p/1p2p3/3pP3/3P4/PP3PPP/4K2R}{S:e1d2}{W:10_15C}Correct. The smarter move is 1. Ke1-d2, keeping the king in the center so that it can prevent the Black rook from invading at c2. Moreover, with the king at d2, White now has the ability to offer a rook trade at c1, if he should deem this desirable. We have to be careful not to follow chess principles too mechanically. They can serve as helpful guidelines and directors, but they don't confer actual knowledge of the position in front of you. Only concrete analysis can do that.}]

16.
[{F:B}{B:40/pKn2k2/16}{QB:16. Should Black push the pawn or defend it?{W:10_16}{A:Ba3a2}{H1:a2}{W:10_16a}{A:Bc3b5}{H1:b5}{W:10_16b};1... a3-a2;
{F:B}{B:40/pKn2k2/16}{S:a3a2}{W:10_16I}Incorrect. Advancing the pawn (1... a3-a2) looks menacing, but it sets up a situation where no progress can be made after White retreats the king {S:b3b2}{W:10_16Ia}(2. Kb3-b2). White will draw by transferring his king, to and fro, between {N1:a1b2}{W:10_16Ib}a1 and b2. Is there any way that Black can try to win? In order to pursue this adventure, he will have to free the {N1:c3}{W:10_16Ic}knight from its defensive chore of guarding the a-pawn, which means the Black king must be brought over to {N1:b3a3}{W:10_16Id}b3 or a3 to protect the pawn. This will free the knight, all right, but it will deny the White king a safe move, which means that White is stalemated. Set this up on your own board and see what I mean. That is, place the Black king on b3 or a3, the Black pawn on a2, and the Black knight on c3. Then put the White king on a1, and make it White's move. He doesn't have one, and it's not check, so this is stalemate.;
1... Nc3-b5;{F:B}{B:40/pKn2k2/16}{S:c3b5}{W:10_16C}Correct. Guarding the pawn (1... Nc3-b5) insures the pawn's safety and the ultimate win, mainly because the Black king is now able to defend the a-pawn without giving stalemate. Black can do this because the pawn remains on its 6th rank, which gives White some breathing room. Once Black's king takes the reigns, and the knight is free to move, it doesn't take long to promote the pawn and deliver mate. A sample variation might go, {S:b3a2}{W:10_16Ca}2. Kb3-a2 {S:f3e3}{W:10_16Cb}Kf3-e3  {S:a2b3}{W:10_16Cc}3. Ka2-b3 {S:e3d3}{W:10_16Cd}Ke3-d3  {S:b3a2}{W:10_16Ce} 4. Kb3-a2 {S:d3c3}{W:10_16Cf}Kd3-c3 {S:a2b1}{W:10_16Cg}5. Ka2-b1 {S:c3b3}{W:10_16Ch}Kc3-b3  {S:b1a1}{W:10_16Ci}6. Kb1-a1. Now Black must be careful. If he blunders with {S:b5c3}{W:10_16Cj}6... Nb5-c3, it's stalemate! But the knight doesn't want to occupy the square c3. Rather it needs to occupy c2, so that it can guard the a1-corner. This is achieved by {F:B}{B:24/1n6/8/pk6/8/K7}{S:b5d4}{W:10_16Ck}6... Nb5-d4. After {S:a1b1}{W:10_16Cl} 7. Ka1-b1, Black checks with the pawn, {S:a3a2}{W:10_16Cm}7... a3-a2+ (or he could play {A:Bd4c2}{W:10_16Cn}7... Nd4-c2 first), and White has the unpleasant choice of moving his king toward the center {R}{A:Bb1c1}{W:10_16Co}(8. Kb1-c1), allowing the pawn to promote to a queen, or of moving the king to the corner {R}{S:b1a1}{W:10_16Cp}(8. Kb1-a1), which ends in immediate mate {S:d4c2}{W:10_16Cq}(8... Nd4-c2#).}]

17.
[{F:B}{B:K7/40/4N1p1/6k1}{QB:17. Should Black get out of check by moving his king to f1 or to f2?{W:10_17}{A:Bg1f1}{H1:f1}{W:10_17a}{A:Bg1f2}{H1:f2}{W:10_17b};1... Kg1-f1;{F:B}{B:K7/40/4N1p1/6k1}{S:g1f1}{W:10_17C}Correct. The game turns in Black's favor after 1... Kg1-f1. This attacks the knight and threatens to make a new queen. White at this point has but one plausible try, and this is to give check again, at knight-three {S:e2g3}{W:10_17Ca}(2. Ne2-g3+). But Black can end the checks once and for all by {S:f1e1}{W:10_17Cb}2... Kf1-e1. With the checks all gone, so is White's aspiration to stop the pawn, which queens by force. This shows the problem of the knight when it comes to dealing with wing pawns, here, a knight-pawn in particular. As the knight approaches the edge of the board, it runs out of maneuvering space, and certain tactical possibilities are no longer available. In order to draw in our given example, there would have to be a ninth file, so that the knight could transfer from g3 to i2. In this way it could guard g1, thwarting the planned queening. But the i-file doesn't exist, nor does Black have any hope of stopping the coronation of White's g-pawn.;
1... Kg1-f2;{F:B}{B:K7/40/4N1p1/6k1}{S:g1f2}{W:10_17I}Incorrect. It's easy to be careless. In Black's desire to escape the checks, he could brashly play the mistake, 1... Kg1-f2. This ends the checks for now, but it doesn't insure the win, for White has the tricky rejoinder, {S:e2f4}{W:10_17Ia}2. Ne2-f4!, which attacks the pawn directly. Since White is quite happy to give up the knight to stop the pawn, Black must promote. But after doing so {S:g2g1}{P:BQg1}{W:10_17Ib}(say 2... g2-g1/Q), White has the forking check, {S:f4h3}{W:10_17Ic}3. Nf4-h3+, and the queen is taken next move. After {S:f2f1}{W:10_17Id}4. Kf2-f1 {S:h3g1}{W:10_17Ie}Nh3xg1  {S:f1g1}{W:10_17If}5. Kf1xg1, the game is drawn by insufficient mating material. Actually the draw could be claimed after White takes the queen {F:B}{B:K7/48/5kN1}{W:10_17Ig}(4... Nh3xg1), before his knight is seized (5. Kf1xg1), because at this point neither player has enough material left to force checkmate.}]

18.
[{F:B}{B:1B6/1k6/1N6/8/PK6/24}{QB:18. Should Black take the bishop or the knight?{W:10_18}{A:Bb7b8}{H1:b8}{W:10_18a}{A:Bb7b6}{H1:b6}{W:10_18b};1... Kb7xb8;
{F:B}{B:1B6/1k6/1N6/8/PK6/24}{S:b7b8}{W:10_18I}Incorrect. Taking the bishop (1... Kb7xb8) is erroneous. It allows White to win with virtually no difficulty, for even though White has a rook-pawn, the least ennobled of all the pawns, White's king and knight will work harmoniously as a team to clear the pawn's path. Most importantly, the knight can guard the a8-corner, preventing Black from seeking a successful blockade and eventual stalemate. The dark-square bishop, on the other hand, can't guard a8, and in this ending that's a real failing.;
1... Kb7xb6;{F:B}{B:1B6/1k6/1N6/8/PK6/24}{S:b7b6}{W:10_18C}Correct. The right piece to take is the knight (1... Kb7xb6), which leaves White with a bishop that can't guard the corner square (a8). White has the so-called "wrong bishop," and the game is positionally drawn. This becomes obvious in the line, 1... Kb7xb6 {S:a4a5}{W:10_18Ca}2. a4-a5+ {S:b6a6}{W:10_18Cb}Kb6-a6 (note the bishop can't influence this light square either) {S:b8f4}{W:10_18Cc}3. Bb8-f4 (for instance) {S:a6b7}{W:10_18Cd} 3... Ka6-b7  {S:b4b5}{W:10_18Ce}4. Kb4-b5 {S:b7a7}{W:10_18Cf}Kb7-a7  {S:a5a6}{W:10_18Cg}5. a5-a6 {S:a7a8}{W:10_18Ch} Ka7-a8, when a further advance of the White king {A:Wb5b6}{W:10_18Ci}(6. Kb5-b6) is not feasible because of the stalemate. So White must get the bishop off the {N1:b8c7d6e5f4g3h2}{W:10_18Cj}b8-h2 diagonal. The game might then go,{C}{R}{S:f4e3}{W:10_18Ck}6. Bf4-e3 {S:a8b8}{W:10_18Cl}Ka8-b8  {S:b5b6}{W:10_18Cm}7. Kb5-b6 {S:b8a8}{W:10_18Cn}Kb8-a8, and no more progress can be made, in that stalemate is given by advancing the pawn to a7. After {W:10_18Co}7... Kb8-a8, White can try various things, but he can't force the Black king from the corner. To do this he'd need a knight or a good bishop -- here, one that travels on light squares. Then a8 could be guarded, and the promotion of the a-pawn rendered certain.}]

19.
[{F:B}{B:8/2kB2b1/3B4/3P4/4PK2/24}{QB:19. Which bishop should Black take?{W:10_19}{A:Bc7d7}{H1:d7}{W:10_19a}{A:Bc7d6}{H1:d6}{W:10_19b};the one on d7;{F:B}{B:8/2kB2b1/3B4/3P4/4PK2/24}{S:c7d7}{W:10_19I}Incorrect. Don't take the bishop on d7 (1... Kc7xd7). This capture allows White the ability to counter Black's dark-square bishop with White's own bishop, denying Black the chance to set up a blockade on the dark squares. After {S:e4e5}{W:10_19Ia}2. e4-e5 {S:g7h6}{W:10_19Ib}Bg7-h6+ {S:f4f5}{W:10_19Ic}3. Kf4-f5, White will be able to escort the pawns to victory. A possible continuation might be, {S:h6d2}{W:10_19Id}3... Bh6-d2 {S:d6c5}{W:10_19Ie}4. Bd6-c5 {S:d2e1}{W:10_19If}Bd2-e1 {S:e5e6}{W:10_19Ig}5. e5-e6+ {S:d7e8}{W:10_19Ih}Kd7-e8 {S:d5d6}{W:10_19Ii}6. d5-d6 {S:e1h4}{W:10_19Ij}Be1-h4 {S:d6d7}{W:10_19Ik}7. d6-d7+ {S:e8d8}{W:10_19Il}Ke8-d8, which ends in mate via {S:c5b6}{W:10_19Im}8. Bc5-b6+ {S:d8e7}{W:10_19In}Kd8-e7 {S:d7d8}{P:WQd8}{W:10_19Io}9. d7-d8/Q#.;
the one on d6;{F:B}{B:8/2kB2b1/3B4/3P4/4PK2/24}{S:c7d6}{W:10_19C}Correct. Taking the dark-square bishop (1... Kc7xd6) creates opposite color bishops, where the White and Black bishops travel on squares of different color. In general, this situation often enables the defender to draw, even when behind by a couple of pawns, because of the possibility of a blockade. In such a scenario, both the defending king and bishop may be able to work together to control squares that the opposing bishop can't contest. This could effectively stop the advance of the enemy pawns, reducing the game to a practical draw. Thus, after 1... Kc7xd6, Black can draw by transferring his bishop, back and forth, along the {N1:a1b2c3d4e5f6g7h8}{W:10_19Ca}a1-h8 diagonal, and there's nothing that White or his bishop can do about it. Black's {N1:d6}{W:10_19Cb}king prevents the {N1:d5}{W:10_19Cc}d-pawn from moving, and the {N1:e4}{W:10_19Cd}e-pawn can never move because it would be taken for free. The game is drawn, plain and simple, for no progress can be made.}]

20.
[{F:W}{B:8/3P1k2/2q5/6K1/7P/24}{QB:20. Should White promote to a queen or something else?{A:Wd7d8}{H1:d8}{W:10_20};to a queen;
{B:8/3P1k2/2q5/6K1/7P/24}{S:d7d8}{P:WQd8}{W:10_20I}Incorrect. The automatic move is to make a new queen (1. d7-d8/Q), but this ends in a draw after {S:c6g6}{W:10_20Ia}1... Qc6-g6+  {S:g5f4}{W:10_20Ib}2. Kg5-f4 {S:g6f6}{W:10_20Ic}Qg6-f6+, forcing the trade of queens and leaving White with a rook-pawn that Black's king can blockade. A possible conclusion might be, {S:d8f6}{W:10_20Id}3. Qd8xf6 {S:f7f6}{W:10_20Ie}Kf7xf6 {S:h4h5}{W:10_20If}4. h4-h5 {S:f6g7}{W:10_20Ig}Kf6-g7 {S:f4g5}{W:10_20Ih}5. Kf4-g5 {S:g7h7}{W:10_20Ii}Kg7-h7 {S:h5h6}{W:10_20Ij}6. h5-h6 {S:h7h8}{W:10_20Ik}Kh7-h8 {S:g5g6}{W:10_20Il}7. Kg5-g6 {S:h8g8}{W:10_20Im}Kh8-g8 {S:h6h7}{W:10_20In}8. h6-h7+ {S:g8h8}{W:10_20Io}Kg8-h8, {S:g6h6}{W:10_20Ip}and 9. Kg6-h6 is stalemate. Once again, sometimes more is less.;
to something else;{B:8/3P1k2/2q5/6K1/7P/24}{W:10_20C}Correct. Sometimes less is more. White wins, not by promoting to a queen, but by making a knight {S:d7d8}{P:WNd8}{W:10_20Ca}(1. d7-d8/N+!). This is a forking check, attacking Black's queen and king simultaneously. After Black gets out of check{S:f7f8}{W:10_20Cb}, White's new knight removes the queen {S:d8c6}{W:10_20Cc}(2. Nd8xc6). Even though White is left with a rook-pawn, usually the weakest type of pawn, the White king and knight will be able to convoy it home without breaking a sweat.}]

21.
[{B:1R6/32/5pk1/r7/6K1}{QB:21. Should White stop mate or check the Black king?{W:10_21}{A:Wb8b1}{H1:b1}{W:10_21a}{A:Wb8g8}{H1:g8}{W:10_21b};
1. Rb8-b1;{B:1R6/32/5pk1/r7/6K1}{S:b8b1}{W:10_21I}Incorrect. Withdrawing the rook to the home rank (1. Rb8-b1) does one important thing. It thwarts the Black mate threat at a1. But it doesn't provide White with any counterpunch, and now he's reduced to shifting his rook along the first rank, waiting for Godot. Meanwhile, Black can head toward a win with {S:a2g2}{W:10_21Ia}1... Ra2-g2+. Now it doesn't matter where White goes with his king. If he moves it to the corner {S:g1h1}{W:10_21Ib}(2. Kg1-h1), Black checks {S:g2h2}{W:10_21Ic}(2... Rg2-h2+), the king skids out of check {S:h1g1}{W:10_21Id}(3. Kh1-g1), and then the pawn advances {S:f3f2}{W:10_21Ie}(3... f3-f2+), with fatal consequences. White can flee from the pawn check {S:g1f1}{W:10_21If}(4. Kg1-f1), but he can't save his rook after the skewering check, {S:h2h1}{W:10_21Ig}4... Rh2-h1+, when it's captured for free next move {S:f1e2}{W:10_21Ih}(5. Kf1-e2 {S:h1b1}{W:10_21Ii}Rh1xb1). Nor does it help if White answers 1... Ra2-g2+ by avoiding the corner in favor of f1 {B:40/5pk1/6r1/1R4K1}{S:g1f1}{W:10_21Ij}(2. Kg1-f1), for Black's rook moves to the h-file anyway {S:g2h2}{W:10_21Ik}(2... Rg2-h2), which threatens to move to h1, giving both a skewer as well as a mate. White can do no better than to move his king rearward to g1 {S:f1g1}{W:10_21Il}(3. Kf1-g1), and this gets us back into the previous variation, which ended with {S:f3f2}{W:10_21Im}3... f3-f2+, etc. Clearly, given our starting position, a passive defense with the rook doesn't make it.;
1. Rb8-g8+;{B:1R6/32/5pk1/r7/6K1}{S:b8g8}{W:10_21C}Correct. To draw, White's rook must stay active. It should do all it can to harass the Black king, beginning with a check along the back rank (1... Rb8-g8+). To this counter, there is no adequate response. Black, of course, can escape the check {S:g3f4}{W:10_21Ca}(let's say 1... Kg3-f4), but White has a new check, {S:g8f8}{W:10_21Cb}2. Rg8-f8+, and again Black must delay his own plans to extricate his king {S:f4e3}{W:10_21Cc}(say 2... Kf4-e3). Another rook check {S:f8e8}{W:10_21Cd}(3. Rf8-e8+) will point out Black's problem, he has no way to end the checks for good. Indeed, White can't do anything other than give checks, but they are good enough to prevent Black from fulfilling his own aims, and the game is drawn. The active rook -- here, the rook with the ability to threaten the enemy king -- saves the day.}]

22.
[{F:B}{B:7R/k6P/16/5K2/8/6r1/8}{QB:22. How should Black attack the pawn?{W:10_22}{A:Bg2g7}{H1:g7}{W:10_22a}{A:Bg2h2}{H1:h2}{W:10_22b};1... Rg2-g7;{F:B}{B:7R/k6P/16/5K2/8/6r1/8}{S:g2g7}{W:10_22I}Incorrect. Attacking the pawn by moving the rook to Black's second rank (1... Rg2-g7) is blunderous. It loses immediately, for White can move his own rook with a gain of time, {S:h8a8}{W:10_22Ia}2. Rh8-a8+. True, this surrenders the White rook for free {S:a7a8}{W:10_22Ib}(2... Ka7xa8), but the sacrifice is quite ephemeral, for after White promotes the h-pawn to a queen {S:h7h8}{P:WQh8}{W:10_22Ic}(3. h7-h8/Q+), Black finds himself in check. Worse than this, it's a fork, and after Black escapes the check {S:a8b7}{W:10_22Id}(3... Ka8-b7), he loses his rook to the newly formed queen {S:h8g7}{W:10_22Ie}(4. Qh8xg7+).;
1... Rg2-h2;{F:B}{B:7R/k6P/16/5K2/8/6r1/8}{S:g2h2}{W:10_22C}Correct. Stationing the Black rook behind the passed pawn (1... Rg2-h2!) sets up a draw. Now White can't sacrifice his rook with a time-gaining check at a8 {S:h8a8}{W:10_22Ca}(2. Rh8-a8+), for after the Black king takes the rook {S:a7a8}{W:10_22Cb}(2... Ka7xa8), Black's own rook is in perfect position (behind the passed pawn) to halt the h-pawn's advance. So how can White try to win? If he attempts to bring his king over to the pawn to protect it, hoping to free his cornered  rook, the Black rook can check ceaselessly. And if White shifts gears, and aims to bring his king back toward Black's rook, Black just keeps his rook on the h-file, making sure to stay far away from White's pestering king. No progress can be made, and the game ends in a positional draw. A corroborating variation (among the vast number of them) is {F:B}{B:7R/k6P/16/5K2/8/6r1/8}{S:g2h2}{W:10_22Cc}1... Rg2-h2 {S:f4g3}{W:10_22Cd}2. Kf4-g3 {S:h2h6}{W:10_22Ce}Rh2-h6  {S:g3g4}{W:10_22Cf}3. Kg3-g4 {S:h6h1}{W:10_22Cg}Rh6-h1  {S:g4g5}{W:10_22Ch}4. Kg4-g5 {S:h1h2}{W:10_22Ci}Rh1-h2  {S:g5g6}{W:10_22Cj}5. Kg5-g6 (this move unburdens White's rook, so Black must act with dispatch) {S:h2g2}{W:10_22Ck}7... Rh2-g2+  {S:g6f5}{W:10_22Cl}6. Kg6-f5 {S:g2f2}{W:10_22Cm}Rg2-f2+  {S:f5g4}{W:10_22Cn}7. Kf5-g4 {S:f2h2}{W:10_22Co}Rf2-h2  {S:g4g3}{W:10_22Cp}8. Kg4-g3 {S:h2h1}{W:10_22Cq}Rh2-h1  {S:g3g2}{W:10_22Cr}9. Kg3-g2 {S:h1h6}{W:10_22Cs}Rh1-h6, and White has gotten nowhere. The game is a practical draw.}]

23.
[{F:B}{B:1R6/8/3k4/24/1p3K2/1r6}
{QB:23. Should Black move his rook or king?{W:10_23}{A:Bb1h1}{H1:h1}{W:10_23a}{A:Bd6e5}{H1:e5}{W:10_23b};1... Rb1-h1;{F:B}{B:1R6/8/3k4/24/1p3K2/1r6}{S:b1h1}{W:10_23C}Correct. Black has an instant win with, 1... Rb1-h1!, clearing the b1-square and threatening to make a new queen with the rook's support. White has little choice but to take the pawn {S:b8b2}{W:10_23Ca}(2. Rb8xb2), whereupon Black delivers a check at h2 {S:h1h2}{W:10_23Cb}(2... Rh1-h2+). This check is also a skewer, and after White moves his king out of check {S:f2f3}{W:10_23Cc}, the Black rook takes the White rook for nothing {S:h2b2}{W:10_23Cd}(3... Rh2xb2).;
1... Kd6-e5;{F:B}{B:1R6/8/3k4/24/1p3K2/1r6}{S:d6e5}{W:10_23I}Incorrect. Moving the king toward the center (1... Kd6-e5) is worse than a misdemeanor. It allows White to set up a drawn position by sidling his king over to g2 {S:f2g2}{W:10_23Ia}(2. Kf2-g2), which guards h1 and stops the Black rook from sneaking around to h1, to set up a decisive skewer. And now there's no way to win. White's king prevents tactical tricks, and his rook is splendidly poised behind the passed pawn to prevent the Black rook from moving without abandoning the b-pawn. Nor is Black's king safe from annoyance, for it can be checked by White's rook whenever the circumstances require it. An exemplary variation is, {F:B}{B:1R6/8/3k4/24/1p3K2/1r6}{S:d6e5}{W:10_23Ib}1... Kd6-e5?  {S:f2g2}{W:10_23Ic}2. Kf2-g2! {S:e5d4}{W:10_23Id}Ke5-d4  {S:g2h2}{W:10_23Ie}3. Kg2-h2 {S:d4c3}{W:10_23If}Kd4-c3 {S:b8c8}{W:10_23Ig}4. Rb8-c8+ {S:c3d4}{W:10_23Ih}Kc3-d4 {S:c8d8}{W:10_23Ii}5. Rc8-d8+ {S:d4c5}{W:10_23Ij}Kd4-c5 {S:d8c8}{W:10_23Ik}6. Rd8-c8+ {S:c5b6}{W:10_23Il}Kc5-b6 {S:c8b8}{W:10_23Im}7. Rc8-b8+ {S:b6c7}{W:10_23In}Kb6-c7 {S:b8b3}{W:10_23Io}8. Rb8-b3 {S:c7c6}{W:10_23Ip}Kc7-c6 {S:b3b8}{W:10_23Iq}9. Rb3-b8 {S:c6c5}{W:10_23Ir}Kc6-c5 {S:h2g2}{W:10_23Is}10. Kh2-g2, and the game is utterly drawable.}]

24.
[{F:W}{B:K7/QPq5/7k/16/4P3/16}{QB:24. Should White make a new queen or check the Black king?{W:10_24}{A:Wb7b8}{H1:b8}{W:10_24a}{A:Wa7a6}{H1:a6}{W:10_24b};
1. b7-b8/Q;{B:K7/QPq5/7k/16/4P3/16}{S:b7b8}{P:WQb8}{W:10_24I}Incorrect. You shouldn't be too hasty when on the verge of victory. Promoting at once (1. b7-b8/Q?) may look inspiring, but clearly it proves injurious to White as Black is able to give a perpetual check, starting with {S:c7c6}{W:10_24Ia}1... Qc7-c6+. It doesn't matter which queen White uses to block the check, for Black can continue issuing checks unendingly from then on. Black can't win, but he can prevent White from doing so, and the game therefore is drawn. An illustrative variation might go, {B:K7/QPq5/7k/16/4P3/16}{S:b7b8}{P:WQb8}{W:10_24Ib}1. b7-b8/Q {S:c7c6}{W:10_24Ic}Qc7-c6+ {S:a7b7}{W:10_24Id}2. Qa7-b7 {S:c6a4}{W:10_24Ie}Qc6-a4+ {S:b8a7}{W:10_24If}3. Qb8-a7 {S:a4e8}{W:10_24Ig}Qa4-e8+ {S:b7b8}{W:10_24Ih}4. Qb7-b8 {S:e8c6}{W:10_24Ii}Qe8-c6+  {S:b8b7}{W:10_24Ij}5. Qb8-b7 {S:c6e8}{W:10_24Ik}Qc6-e8+ {S:a7b8}{W:10_24Il} 6. Qa7-b8 {S:e8a4}{W:10_24Im}Qe8-a4+ {S:b7a7}{W:10_24In}7. Qb7-a7 {S:a4c6}{W:10_24Io}Qa4-c6+, and this ring-around-the-rosey approach gets nowhere. The game is drawn by perpetual check, confirming the fact that an extra queen doesn't always win.;
1. Qa7-a6+;{B:K7/QPq5/7k/16/4P3/16}{S:a7a6}{W:10_24C}Correct. If White keeps his eyes open, he delays promoting in favor of a security check, 1. Qa7-a6+!. Wherever Black moves his king to get out of the check {S:h6g5}{W:10_24Ca}(say 1... Kh6-g5), White can then promote {S:b7b8}{P:WQb8}{W:10_24Cb}(2. b7-b8/Q), and Black doesn't have a single safe check, let alone a full perpetual. No matter how Black uses his second move, White's material superiority will soon bring down the Black king. Occasionally, you have to show a little patience.}]

25.
[{B:7k/8/4p3/8/p4q1P/P7/KP2QP1P/8}{QB:25. Should White take a pawn or give a check?{W:10_25}{A:We2e6}{H1:e6}{W:10_25a}{A:We2h5}{H1:h5}{W:10_25b};1. Qe2xe6;
{B:7k/8/4p3/8/p4q1P/P7/KP2QP1P/8}{S:e2e6}{W:10_25I}Incorrect. This is no time to be materialistic. Taking the king-pawn (1. Qe2xe6) is unreasonably greedy. It also stumbles into Black's unexpected saving grace, {S:f4f7}{W:10_25Ia}1... Qf4-f7!. To this bold stroke, which pins the White queen to its king, White has no choice but to accept the sacrifice, {S:e6f7}{W:10_25Ib}2. Qe6xf7. But taking the queen leaves Black without a single move, and according to the rules of chess, this is stalemate. The game is drawn, and once again we see that more can turn out to be less.;
1. Qe2-h5+;{B:7k/8/4p3/8/p4q1P/P7/KP2QP1P/8}{S:e2h5}{W:10_25C}Correct. When ahead in material, the general policy should be to trade pieces, simplifying the position. In this way your extra material begins to mean more. White can force a winning queen trade with 1. Qe2-h5+. Black must move his king to the g-file {S:h8g7}{W:10_25Ca}(1... Kh8-g7), whereupon White checks at g5 {S:h5g5}{W:10_25Cb}(2. Qh5-g5+), and the queens come off the board {S:f4g5}{W:10_25Cc}(2... Qf4xg5 {S:h4g5}{W:10_25Cd}3. h4xg5), denying Black his best counterplayer - his queen. Now Black will be unable to cope with White's two-theater advantage, for White has extra pawns on both sides of the board. Concluding proof is provided by this variation, {S:g7g6}{W:10_25Ce}3... Kg7-g6 (attacking the g-pawn) {S:h2h4}{W:10_25Cf}4. h2-h4 (defending the g-pawn) {S:g6h5}{W:10_25Cg}4... Kg6-h5 (but this threatens nothing, for the h-pawn can't be taken without allowing the g-pawn's promotion) {S:b2b4}{W:10_25Ch}5. b2-b4 {S:a4b3}{X:b4}{W:10_25Ci}a4xb3+ {S:a2b3}{W:10_25Cj}6. Ka2xb3, and Black finds himself in the unenviable situation of having to stop pawns on both the queenside and kingside. This can't be done, and so the most prudent continuation is to resign and start another game.}]