Answers 339- ODDS AND EVENS
The fewest possible moves are 24. Playas follows. (It is only necessary to
give, by the letters, the circles from which and to which the counters are
moved. Only a single counter can be moved at a time.) E to A, E to B, E to
C, E to D, B to D, E to B, C to B, A to B, E to C, E to A, B to A, C to E, B
ABC~RCBEE~RC~RD~a
D to B, E to B-24 moves.
- RAILWAY SHUNTING
Make a rough sketch like our diagram and use five counters marked X, L,
R, A, and B. The engines are Land R, and the two cars on the right A and
B. The three cars on the left are never separated, so we call them X. The side-
track is marked S. Now, playas follows: R to left, R to S, XL to right, R to
left, XLA to left, L takes A to S, L to left, XL to right, R to A, RA to left,
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5
XLB to left, L takes B to S, L to left, LX right away, RA to B, RAB
right away. Fourteen moves, because the first and third moves (R to left and
XL to right) do not involve a change of direction. It cannot be done in fewer
moves.- ADJUSTING THE COUNTERS
Make the exchanges of pairs as follows: (1-7, 7-20, 20-16, 16-11, 11-2,
2-24), (3-10, 10-23,23-14, 14-18, 18-5), (14-19, 19-9,9-22), (6-12, 12-15,
15-13,13-25), (17-21). The counters are now all correctly arranged in 19 ex-
changes. The numbers within a pair of brackets represent a complete cycle,