Trivium

The names of two U.S. state capitals end with the same eight letters. What are they?

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Jefferson City, Missouri, and Carson City, Nevada.

March 9, 2014March 16, 2014 | Puzzles · Trivia

Black and White

gold chess problem

By Sámuel Gold. White to mate in two moves.

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With 1. Qf3 White threatens 2. Qh5#. If Black captures the queen then 2. d4 is mate. His only other defenses require moving the bishop (Bxb3/Be6/Bf7), which permits an immediate 2. Qxe4#. From The Chess Players’ Chronicle, 1872.

March 7, 2014March 16, 2014 | Puzzles

“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?

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

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Dutch: aloud — very old, angel — sting, hark — rake, inner — collector, lover — foliage, room — cream, taken — jobs, wig — wedge Finnish: alas — down, atlas — satin, into — enthusiasm, manner — mainland, pore — bubble, tie — road, vain — only, valve — awake French: ail — garlic, ballot — bumpkin, enter — to graft, four — oven, lent — slow, lit — bed, mire — gun sight, teller — to send out roots Japanese: banjo — sovereign, chosen — challenge, hippo — style of calligraphy, pure — pulley, same — shark, share — witticism, tempo — supplement, tendon — bowl of rice and fish Latin: ago — I act, cur — why, dare — to give, fur — thief, limes — boundary, mane — early in the morning, probe — thoroughly, undo — wave

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March 6, 2014March 16, 2014 | Language · Puzzles

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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After 1. Kg1 Black has no safe move: If he moves the king to e4 or f3, then the queen zooms westward to infinity and mates, attacking simultaneously from left and right on every rank. If he moves the king onto the g-file then the queen zooms southwestward to infinity, attacking simultaneously along all the southwest-northeast diagonals from both directions. If he moves the d-pawn then again the queen can mate from the southwest/northeast. If he moves the b6 knight (anywhere), then the queen zooms northwest and attacks along the northwest-southeast diagonals. If he moves the c7 knight then the queen zooms north and attacks along the files. Given all this firepower, White’s main task is really to find a square where his king is safely out of the way. But that’s tricky. After 1. Kh1?, for example, Black has 1. … Nbd5! and there’s no mate.

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March 5, 2014March 16, 2014 | Puzzles

Reunion

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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Yes. The father sets out with his first son, leaving the second boy to walk alone. Father and son drive 24 kilometers, which takes 6/5 hours. Then the father puts down the first son and rides back to meet the second son 9 kilometers from home, which takes 3/5 hours. Finally he and the second son ride 6/5 hours more and reach grandmother’s house just as the first son is arriving there on foot. Each son spends 6/5 hours riding 24 kilometers and 9/5 hours walking 9 kilometers, so the three of them reach grandmother’s in exactly 3 hours.

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March 3, 2014March 9, 2014 | Puzzles

Black and White

By Ottmar Weiß. White to mate in two moves.

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The surprising 1. Qh3! leaves Black with no options. If he moves his knight then White can take the rook with mate, and if he moves the rook then White’s knight will mate. From Teplitz-Schönauer Anzeiger, 1921.

February 28, 2014March 9, 2014 | Puzzles

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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“The two children were so befogged over the calendar that they had started on their way to school on Sunday morning!”

February 24, 2014March 2, 2014 | Puzzles

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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In presenting this problem in Ingenuity in Mathematics, Ross Honsberger gave a complex analysis, but his friend Scott Vanstone showed a simple way to visualize it, building on an observation by John Annulis: Each boy is represented by a point, and each pair of boys named in an accusation are joined by a line. Now we know that each line has a thief at one end and an innocent at the other, except for one line, which has an innocent at both ends (due to the outright liar). Since four boys named one guilty boy correctly, the two points that represent the thieves are attached to a total of four lines. And because no boy made two accurate accusations, the thieves themselves are not joined by a line. The only two points that satisfy all these requirements indicate Charlie and James.

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February 23, 2014March 2, 2014 | Puzzles

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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Yes. First three cannibals cross; then the two rowers return, bearing an extra missionary; then the rowing missionary crosses with a cannibal and returns with two missionaries; and finally the rowing cannibal crosses: Mmmm Cccc MmmmCcc c mmcc MmCc Mmmccc mC ccc MmmmC Cccc Mmmm