A puzzle by David Silverman:

Able, Baker, and Charlie are playing tag. Able is faster than Baker, who’s faster than Charlie. All three of them start at point P, and Able is “it.” At time -T, Baker runs north and Charlie runs south. After a count that takes time T, Able starts chasing one of the two quarries. The game ends when Able has tagged both Baker and Charlie. If Baker and Charlie maintain their speeds and directions, who should Able chase first to minimize the time required to make the second tag?

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Black and White

William Shinkman published this problem in the St. Louis Globe Democrat in 1887. White is to mate in 8 moves:

shinkman chess problem - 1

It’s easier than it sounds — with the right approach, all Black’s moves are forced:

1. O-O-O Kxa7 2. Rd8 Kxa6 3. Rd7 Kxa5 4. Rd6 Kxa4 5. Rd5 Kxa3 6. Rd4 Kxa2 7. Rd3 Ka1 8. Ra3#

shinkman chess problem - 2

Remarkably, though the problem position looks contrived, it’s reachable in a legal game (discovered by Bader Al-Hajiri):

1. g4 e5 2. Nh3 Ba3 3. bxa3 h5 4. Bb2 hxg4 5. Bc3 Rh4 6. Bd4 exd4 7. Nc3 dxc3 8. dxc3 g3 9. Qd3 Rb4 10. Nf4 g5 11. h4 f5 12. h5 d5 13. h6 Bd7 14. h7 g2 15. h8B g1R!! 16. Bd4 Ba4 17. Rh4 Rg3 18. Bg2 gxf4 19. Be3 fxe3 20. Be4 fxe4 21. fxe3 exd3 22. exd3 c5 23. Rc4 dxc4 24. dxc4 b5!! 25. cxb4 Qa5 26. cxb5 Na6 27. bxa5 O-O-O!! 28. bxa6 Rd4 29. exd4 Rb3 30. cxb3 Ne7 31. bxa4 Nd5 32. dxc5 Nb6 33. cxb6 Kb8 34. bxa7+ Ka8

(Thanks, Florian.)


From Martin Gardner: Each of the two equal sides of an isosceles triangle is one unit long. How long must the third side be to maximize the triangle’s area? There’s an intuitive solution that doesn’t require calculus.

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On June 30, 1999, the body of 41-year-old Ricky McCormick was discovered near a cornfield in West Alton, Missouri. He’d last been seen alive five days earlier; now he was 15 miles from home though he owned no car. In his pockets were two handwritten notes (click to enlarge):

In the ensuing 18 years both the FBI’s Cryptanalysis and Racketeering Records Unit and the American Cryptogram Association have failed to find any meaning in these messages. In 2011 the FBI appealed to the public for their insights: If you have any you can contact them via this page.

“We are really good at what we do,” said CRRU chief Dan Olson, “but we could use some help with this one.”

The Grapevine

A problem from the British Columbia Colleges Senior High School Mathematics Contest, 2000:

Not all of the nine members on the student council are on speaking terms. This table shows their relationships — 1 means two members are speaking to each other, and 0 means they’re not:

  A B C D E F G H I
A - 0 0 1 0 0 1 0 0
B 0 - 1 1 1 1 1 1 1
C 0 1 - 0 0 0 1 1 0
D 1 1 0 - 1 0 1 0 1
E 0 1 0 1 - 0 1 0 0
F 0 1 0 0 0 - 0 0 1
G 1 1 1 1 1 0 - 0 0
H 0 1 1 0 0 0 0 - 0
I 0 1 0 1 0 1 0 0 -

Recently councilor A started a rumor, and it was heard by each councilor once and only once. Each councilor heard it from, and passed it to, another councilor with whom she was on speaking terms. If we count councilor A as zero, then councilor E was the eighth and last councilor to hear the rumor. Who was the fourth?

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Murder Most Classificatory

In Anthony Boucher’s short story “QL 696.C9,” a librarian is found dead at her desk. She has been shot, and apparently spent her last moments typing the Library of Congress card catalog number that gives the story its title. The killer evidently saw nothing incriminating in this and so left it alone. The investigators have narrowed the list of suspects to junior librarian Stella Swift, children’s librarian Cora Jarvis, library patron James Stickney, and high school teacher Norbert Utter. Who did it?

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A problem from the British Columbia Colleges Senior High School Contest for 2000:

If I place a 6 cm × 6 cm square on a triangle, I can cover up to 60% of the triangle. If I place the triangle on the square, I can cover up to 2/3 of the square. What is the area, in cm2, of the triangle?

(a) 22 4/5
(b) 24
(c) 36
(d) 40
(e) 60

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