340 Answersall being put in their proper places. Write out the numbers in their original
order, and beneath them in their required order, thus:
7 24 10 19 3 12 20 8 22, etc.
I 2 3 4 5 6 7 8 9, etc.The construction of the cycles is obvious, for I in the bottom row is ex-
changed with the 7 above it, then this 7 with the 20 above it, and so on until
the cycle completes itself, when we come to 24 under 1.
- NINE MEN IN A TRENCH
Let the men move in the following order: 2-1,3-2,4-3,5-11,6-4,7-5,8-6,
9-7,1-13,9-10,8-9,1-12,7-13,6-8,5-7,1-11,4-12,3-6, 2-5, 1-1,2-2,3-3,
4-4,5-5,6-6, 7-7, 8-8, 9-9, and the sergeant is in his place in 28 moves.
The first number in a move is that of a man, and the second number that
of his new position, the places being numbered I to 10 in the row, and the re-
cesses II to 13 above.
- BLACK AND WHITE
In the first case move the pairs in the following order: 67 before the I, then
34, 7 I, and 4 8 to the vacant spaces, leaving the order 64 827 I 5 3.
In the second case move 3 4 and replace them as 4 3 before the I. Then re-
move and reverse 6 7 (as 7 6), 6 5 (as 56),3 I (as I 3), and 6 8 (as 8 6), leaving
the order 4 8 6 2 7 I 3 5-five moves in this case.
378. THE ANGELICA PUZZLE
Though we start with the A's in correct positions, the puzzle can only
be solved by making them change places. Represent the A in the bottom row
with a capital letter, and the A in the top comer with a small letter. Then here
is a solution in 36 moves: A N LEG AN G C I A N G C I AN GeL E a
ANG ILCIL aECaL I (36 moves).
[Dudeney's solution is not minimal. Can the reader find a way to solve it
in 30 moves?-M. G.]