From The Booke of Meery Riddles, 1629:

A soldier that to Black-heath-field went,
Prayed an astronomer of his judgment,
Which wrote these words to him plainly,–
Thou shalt goe thither well and safely
And from thence come home alive againe
Never at that field shalt thou be slaine.
The soldier was slaine there at that field,
And yet the astronomer his promise held.


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Black and White

yarosh chess puzzle

By Alexander Yarosh. The position above was reached in a legal game, except that one piece has been knocked off the board. What was it?

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A problem from the 2004 Moscow Mathematical Olympiad:

An arithmetic progression consists of integers. The sum of its first n terms is a power of two. Prove that n is also a power of two.

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Moving Up

My wife and I walk up an ascending escalator. I climb 20 steps and reach the top in 60 seconds. My wife climbs 16 steps and reaches the top in 72 seconds. If the escalator broke tomorrow, how many steps would we have to climb?

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Pointing Fingers

Only one of these statements is true. Which is it?

A. All of the below
B. None of the below
C. One of the above
D. All of the above
E. None of the above
F. None of the above

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A conundrum by French puzzle maven Pierre Berloquin:

Caroline leaves town driving at a constant speed. After some time she passes a milestone displaying a two-digit number. An hour later she passes a milestone displaying the same two digits but in reverse order. In another hour she passes a third milestone with the same two digits (in some order) separated by a zero.

What is the speed of Caroline’s car?

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Two Olive Problems

1. A friend gives you a bottle that contains seven olives. Two of them are green and five are black. He bets that if you remove three olives at random from the bottle, they’ll include a green one. Should you take the bet?

2. Agnes has a tin of olives. It originally contained both black and green ones, but someone has been eating them, so she’s not sure of the colors of the 14 olives that remain. She removes 7 at random and finds that they’re all green. If the odds of this happening were exactly 50-50, what are the colors of the remaining 7?

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Railway Mazes

In 2000, the residents of Luppitt, East Devon, installed a granite bench decorated with a variety of puzzles and curiosities that “it is hoped will be practical and entertaining for most of the next millennium.”

Among the puzzles is this “railway maze,” contributed by Roger Penrose. Make your way from Start in the upper left to Finish in the lower right. The catch is that your train has no reverse gear — you must move continually forward, following the natural curve of the track and making no sharp turns.

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foursquare puzzle

Print out two copies of this pattern, cut them out, and fold each along the dotted lines, making two identical solids. Then fit these two pieces together to make a regular tetrahedron.

This sounds dead simple, but it stumped me for some time. See if you can do it. (There’s no trick — the task is just what it seems.)