Competing Squares

competing squares

A square has been inscribed in each of two congruent isosceles right triangles. Which square is larger?

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Black and White

tchepizhni chess problem

This problem, by V. Tchepizhni, won fifth prize in the Bohemian Centenary Tourney of 1962. It’s four puzzles in one:

(a) The diagrammed position.
(b) Turn the board 90 degrees clockwise.
(c) Turn the board 180 degrees.
(d) Turn the board 270 degrees clockwise.

Each of the resulting positions presents a helpmate in two: Black moves first, then White, then Black, then White, the two sides cooperating to reach a position in which Black is checkmated. What are the solutions?

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A Stressful Game

A puzzle by Ezra Brown and James Tanton:

Three gnomes sit in a circle. An evil villain puts a hat on each gnome’s head. Each hat is either rouge or puce, the color chosen by the toss of a coin. Each gnome can see the color of his companions’ hats but not of his own.

At the villain’s signal, all three gnomes must speak at once, each either guessing the color of his own hat or saying “Pass.” If at least one of them guesses correctly and none guesses incorrectly, all three gnomes will live. But if any of them guesses incorrectly, or if all three pass, they’ll all die.

They may not communicate in any way during the game, but they can confer beforehand. How can they arrange a 75 percent chance that they’ll survive?

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Secret Message

Jonathan Swift’s Journal to Stella, a collection of 65 letters written to his friend Esther Johnson, contains some puzzling passages, such as this one:

“He gave me al bsadnuk lboinlpl dfaonr ufainfbtoy dpionufnad, which I sent him again by Mr. Lewis.”

How should the obscured phrase be read?

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Black and White

shinkman chess problem

By William Anthony Shinkman. White to mate in two moves.

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