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Puzzle Sum 2

What two cities do these sums spell?

CHIN – N + CAGE – E + O = CHICAGO
ROPE + N – PEN + CHEST + ENGINEER – ENGINE = ROCHESTER

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Samuel Loyd (1841 – 1911), born in Philadelphia and raised in New York City, was an American chess player, chess composer, puzzle author, and recreational mathematician. As a chess composer, he authored a number of chess problems, often with interesting themes. At his peak, Loyd was one of the best chess players in the US and was ranked 15th in the world, according to chessmetrics.com.

Snail on a Tree

A snail is trying to climb a 10-meter poll. Every day it climbs 4 meters up and then during the night slides 3 meters down. How many days are needed for the snail to get to the top of the poll?

Seven days only. After the sixth day, the snail would have climbed 6 meters. During the seventh day, it will climb 4 more meters and will get to the top.

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Marathon

You are running a marathon and right at the finish line, you pass the runner in the 2nd position. In which place do you finish the marathon?

You finish 2nd. Before passing the runner you were at 3rd place.

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Missing Pawns

White to play and mate in 4 moves.

Remark: The position on the diagram is one which occurs in actual play.

Notice that the black queen and the black king have switched positions. However, this can happen only if some pawns have been moved. Therefore we can conclude that the bottom row on the diagram is actually the 8th row of the chessboard. All black and all white pieces have reached their respective opposite sides of the board.

Now White’s first move is Kb8-d7. The only moves black can play are with the knights. If Black plays Kb1-a3, Kb1-c3 or Kg1-h3, white mates in 2 more moves – Kd7-c5 and Kc5-d3. If Black moves Kg1-f3, then after Kd7-c5 Black can delay the mate by playing Kf3-e5. However, after the white queen takes it with Qxe5, Kc5-d3 is unavoidable.

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Mate No Matter What

If White is to play, can he always mate Black in 2 moves, regardless of the moves played before?

The first thing to notice is that since the last move was made by Black, either the king or the rook was moved and therefore Black cannot castle anymore. Now White plays Qa1 and no matter what is Black’s next move, Qh8 gives check-mate.

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