Sources page biographical material

5.R.4. REVERSING FROGS AND TOADS: _12...n TO _n...21 , ETC.
A piece can slide into the empty cell or jump another piece into the empty cell.
Dudeney. AM. 1917.

Prob. 214: The six frogs, pp. 59 & 193. Case of n = 6, solved in 21 moves, which he says is minimal. In general, the minimal solution takes n(n+1)/2 moves, including n steps, when n is even and (n²+3n-8)/2 moves, including 2n-4 steps, when n is odd. "This complete general solution is published here for the first time."

Prob. 215: The grasshopper puzzle, pp. 59 & 193-194. Problem for a circular arrangement. Example has n = 12. Says he invented it in 1900. Solvable in 44 moves. General solution is complex -- he says that for n > 4, it can be done in (n²+4n-16)/4 moves when n is even and in (n²+6n-31)/4 moves when n is odd.

Rohrbough. Puzzle Craft. 1932. The Reversible Frogs, p. 22 (= The Jumping Frogs, pp. 20 21 of 1940s?). n = 8, citing Dudeney, AM.

Robert Harbin. Party Lines. Op. cit. in 5.B.1. 1963. Hopover, p. 89. First gives 3 and 3 Frogs and Toads, then asks for complete reversal from 123_456 to 654_321.

[Henry] Joseph and Lenore Scott. Master Mind Pencil Puzzles. Tempo Books (Grosset & Dunlap), NY, 1973 (& 1978?? -- both dates are given -- I'm presuming the 1978 is a 2nd ptg or a reissue under a different imprint??). Reverse the numbers, pp. 117 118. Give the problem for n = 6 and a solution in 21 moves. For n even, the method gives a solution in n(n+1)/2, it is not shown that this is optimal, nor is a general method given for odd n.

[Henry] Joseph & Lenore Scott. Master Mind Brain Teasers. 1973. Op. cit. in 5.E. 13-hour clock, pp. 43-44. Case n = 12 considered in a circle can be done in 44 moves.

Joe Celko. Jumping frogs and the Dutch national flag. Abacus 4:1 (Fall 1986) 71-73. Cites Dudeney and gives the results.

Jim Howson. The Computer Weekly Book of Puzzlers. Computer Weekly Publications, Sutton, Surrey, 1988, unpaginated. [The material comes from his column which started in 1966, so an item may go back to then.] Prob. 54 -- same as the Scotts in Master Mind Pencil Puzzles.