A puzzle by Henry Dudeney. Frogs sit on eight of these 64 tumblers so that no two occupy the same row, column, or diagonal. “The puzzle is this. Three of the frogs are supposed to jump from their present position to three vacant glasses, so that in their new relative positions still no two frogs shall be in a line. What are the jumps made?” The frogs may not exchange positions; each must jump to a glass that was not previously occupied.
(“But surely there must be scores of solutions?” “I shall be very glad if you can find them. I only know of one — or rather two, counting a reversal, which occurs in consequence of the position being symmetrical.”)
|
SelectClick for Answer |
“The frogs that jump are George in the third horizontal row; Chang, the artful-looking batrachian at the end of the fourth row; and Wilhelmina, the fair creature in the seventh row. George jumps downwards to the second tumbler in the seventh row; Chang, who can only leap short distances in consequence of chronic rheumatism, removes somewhat unwillingly to the glass just above him — the eighth in the third row; while Wilhelmina, with all the sprightliness of her youth and sex, performs the very creditable saltatory feat of leaping to the fourth tumbler in the fourth row. In their new positions it will be found that of the eight frogs no two are in a line vertically, horizontally, or diagonally.”
(Henry E. Dudeney, “The Professor’s Puzzles,” Strand 12:12 [December 1896], 720-726; “The Professor’s Puzzles: Solutions,” Strand 13:1 [January 1897], 106-109.)
|
