Black and White

shinkman chess problem

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

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“Anglo-Foreign Words”

Walter Penney of Greenbelt, Md., offered this poser in the August 1969 issue of Word Ways: The Journal of Recreational Linguistics. Below are five groups of English words. Each group appears also in a foreign language. What are the languages?

  1. aloud, angel, hark, inner, lover, room, taken, wig
  2. alas, atlas, into, manner, pore, tie, vain, valve
  3. ail, ballot, enter, four, lent, lit, mire, taller
  4. banjo, chosen, hippo, pure, same, share, tempo, tendon
  5. ago, cur, dare, fur, limes, mane, probe, undo
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Projective Chess

In projective geometry, every family of parallel straight lines intersects at an infinitely distant point. Chess problem composers in the former Yugoslavia have adapted this idea for the chessboard, adding four special squares “at infinity.”

projective chess 1

Now a queen on a bare board, for example, can zoom off to the west (or east) and reach a square “at infinity” from which she attacks every rank on the board simultaneously from both directions. She might also zoom to the north (or south) to reach a different square at infinity; from this one she attacks every file simultaneously, again from both directions. Finally she can zoom to the northwest or southeast and attack all the diagonals parallel to a8-h1, or zoom to the northeast or southwest and attack all the diagonals parallel to a1-h8. These four “infinity squares,” plus the regular board, make up the field of play.

N. Petrovic created the problem below, published in Matematika Na Shahmatnoi Doske. White is to play and mate in at least two moves. Can you find the solution?

projective chess 2

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Reunion

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A Russian problem from the 1999 Mathematical Olympiad:

A father wants to take his two sons to visit their grandmother, who lives 33 kilometers away. His motorcycle will cover 25 kilometers per hour if he rides alone, but the speed drops to 20 kph if he carries one passenger, and he cannot carry two. Each brother walks at 5 kph. Can the three of them reach grandmother’s house in 3 hours?

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Calendar Trouble

From Sam Loyd:

Two children, who were all tangled up in their reckoning of the days of the week, paused on their way to school to straighten matters out.

“When the day after tomorrow is yesterday,” said Priscilla, “then ‘today’ will be as far from Sunday as that day was which was ‘today’ when the day before yesterday was tomorrow!”

On which day of the week did this puzzling prattle occur?

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Crime Story

Six boys are accused of stealing apples. Exactly two are guilty. Which two? When the boys are questioned, Harry names Charlie and George, James names Donald and Tom, Donald names Tom and Charlie, George names Harry and Charlie, and Charlie names Donald and James. Tom can’t be found. Four of the boys who were questioned named one guilty boy correctly and one incorrectly, and the fifth lied outright. Who stole the apples?

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Playing With Food

A group of four missionaries are on one side of a river, and four cannibals are on the other side. The two groups would like to exchange places, but there’s only one rowboat, and it holds only three people, and only one missionary and one cannibal know how to row, and the cannibals will overpower the missionaries as soon as they outnumber them, either on land or in the boat. Can the crossing be accomplished?

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