Old Solutions

Solution for 10/21/2018

Following is the game score with notes from today's puzzler, to better understand the solution; you can click and move through below:

Solution: 6/3/2018

Solutions: 7/16/2017

Answer 1 (A1)

Additional Note: today's puzzle was particularly hard! If you solved it, you deserve a pat on the back :)

Below are some relevant variations from today's puzzler.  The careful observer will notice that a back rank mate is threatened on a few occasions, and several variations include skewer threats (attacking the king with the rook, forcing it to move, in turn winning the opposing rook).

Answer 2 (A2)

35.Re8+! and Black resigned in light of either 35. ... Rxe8 36.Qxd5 or 35. ... Kh7 36.Rxd8

More Explained: 6/18

Retaining the opposition (distant or close) for Black in this case can be thought of as a complicated version of Simon says. One false move, and White's king invades.  Play the game correctly, and the White king will always be forced to step aside and never gain access to critical squares.

One consideration not mentioned in the paper (due to lack of space) is White playing h5 at any point, which appears to give White the opposition. Problem is, there is no way to exploit that opposition with the backward g4 pawn.  Consider one variation below:

Additionally, here is some general king and pawn opposition theory for those who may not have seen it before:

Contrariwise, if the White king was in front of the pawn AND White retained the opposition (meaning, White can make the Black king step aside, i.e. Black to move below), then this would be a loss for Black:

Solution for 5/28

Correction Note:
 today's column had superscripts removed by the editors. The answer should have read: 

"There are 204 squares on a chessboard. 8^2 = 64 1x1 squares, plus 7^2 = 49 2x2 squares, plus 6^2 = 36 3x3 squares, etc. for a sum of squares: 8^2 + 7^2 + 6^2 + 5^2 + 4^2 + 3^2 + 2^2 + 1^2 = 204 squares."

There are 15 checkmates: Nd3#, Nc6#, Nf3#, Ng6#, Qh8#, Qfg7#, Qfe7#, Qff5#, Qf4#, Qfd6#, Qde7#, Qdd6#, Qdf5#, Qde8#, and Qd5#. You can move through them all below.

Also, Nigel Coldwell (who seems to specialize in math puzzles) provides a nice extended discussion re. the squares on a chessboard problem here.

Supplemental to Solution: 5/14

The answer is 22.Qc1; however, Black has one interesting reply not covered in the newspaper.  You can move through relevant variations below:

Solution for 4/9

You can move through pertinent variations below:

Solution for 4/2 Explained

Answer: f6

But why?

f6 is possible, despite the double check from the Ba1 and Qf3, because of f5xe6 en passant, discovering two checks at once.  It can be inferred that the pawn push by Black was provoked by a discovered check from the knight currently on g6.

Let's take a look at why all other squares aren't possible, one grouping at a time.

First, it is amusing to notice that aside from Black's e-pawn, all pieces from the start of the game are intact.  This means that any square along the 8th rank or 1st rank is impossible, because (1) there are no plausible discovered checks along either rank from this position, and (2) there are no possible previous captures on the home ranks by either rook.

All squares adjacent to the White king can be immediately dismissed, in addition to all squares attacked by White pawns on their home rank. b2, c3, and d4, and e5 can be dismissed for lack of a possible discovery revealing check from the Ba1. e7, g4, f4, f5, and c4 can be dismissed because they would implicate impossible double checks. e2 is special. It almost seems to be a plausible square, if White's last move was capturing with the queen on f3.  Problem is, the only piece missing is the Black e-pawn, so a capture on f3 is not possible.

This only leaves the f6 square as a possibility.  If you still don't believe this position can be obtained via a series of legal moves, I invite you to go through a sample game proving legality:

Solution for 3/12

1. Bh1!
A) If the R moves along the first rank or d2, e.g.: 1. ... Rxh1 2.Nd2#
B) If the Black knight moves, e.g.: 1... Nc3 2. Nc5#
C) 1... Rd3 2. Rf4#
D) 1... d3 2. Rf4#
E) 1... f5 2. Re3#