Jumping Kangaroos

A puzzle by National Security Agency mathematician David B., from the agency’s October 2017 Puzzle Periodical:

Joey, the baby kangaroo has been kidnapped and placed at 2100 on a number line.

His mother, Kandice the Kangaroo, is at 0 on the number line, and will try to save him. Kandice normally jumps forward 6 units at a time. Guards have been placed at n3 on the number line, for every integer n≥1. If Kandice lands on a number with a guard on it, she will be caught and her mission will fail. Otherwise, she will safely sneak past the guard. Whenever she successfully sneaks past a guard, she gets an adrenaline rush that causes her next jump (the first jump after passing the guard) to take her 1 unit farther than it normally would (7 units instead of 6). (After a single 7-unit jump, she resumes jumping 6 units at a time, until the next time she sneaks past a guard.)

Will Kandice the Kangaroo reach (or pass) her son Joey safely?

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Current Affairs

A problem by G. Galperin, from the May-June 1995 issue of Quantum:

A raft and a motorboat depart simultaneously from Point A on a riverbank and begin drifting and speeding downstream, respectively, toward Point B. At the same moment, a second motorboat, of the same type as the first, sets out from Point B heading upstream. When the first motorboat reaches B, will the floating raft be closer to Point A or to the second motorboat?

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Odd Job

A problem by Russian mathematician Viktor Prasolov:

On a piece of graph paper, is it possible to paint 25 cells so that each of them has an odd number of painted neighbors? (“Neighboring” cells have a common side.)

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The Sure Thing

In a 1905 short story by Jacob Elson, Mr. Brown laments that he cannot solve chess problems.

Mr. Pincus wagers $10 that “I can show you a two-move problem with three different lines of play which you would have to solve whether you wanted to or not.”

Brown accepts. After studying the board for 10 minutes, he says, “It’s a humbug, a confounded silly swindling humbug, but I am beat.” Here’s the position:

sure thing chess position

The Studious Bather

A puzzle from Chris Maslanka’s The Pyrgic Puzzler, 1987:

A bathtub will fill in 3 minutes if the plug is in and the cold tap only is turned on full. It will fill in 4 minutes if the plug is in and the hot tap only is turned on full. With the plug out and both taps off, a full tub will drain in 2 minutes. How long will it take to fill the empty tub if the plug is out and both taps are turned on full?

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Row and Columns

A problem from the 2011 Moscow Mathematical Olympiad: In a certain square matrix, the sum of the two largest numbers in each row is r and the sum of the two largest in each column is c. Show that r = c.

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Backward Baseball

In a retrograde analysis puzzle, one tries to deduce the history of a game from the current state of play. The most familiar examples concern chess, but Smith College mathematician Jim Henle worked out that it can also be done in baseball. This is the batting order of the Mudville Slugs:

  1. Flynn
  2. Blake
  3. Casey
  4. Hobbes
  5. Davis
  6. Shlabotnick
  7. Thayer
  8. Cooney
  9. Barrows

We’re told also that in the ninth inning Casey came to bat for the fourth time, while the bases were loaded with two men out. Casey struck out, leaving the team with another loss. How many runs did Mudville score altogether?

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Black and White

morse chess problem

By Christopher Jeremy Morse. White to mate in two.

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