Tails Up: (E. Hordern, CFF 43, 1997)
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A coin problem from a recent article in Quark (a Japanese publication).
Start and end with the four coins positioned as the figure.
A move consists in one coin jumping one or more others: up,
down, left, right and/or diagonally. There must be a space to land
on after each coin jumped. Every time a coin is jumped, turn it over.
Starting with all the coins "heads up", reverse all the coins
in five moves - "tails up".
The puzzle is not nearly so easy as it looks.
. . . . .
. . O O .
. O O . .
. . . . . the 4 coins in the starting position
Hint1:
- as each coin jumps only an even number of row or columns
we have the pattern:
A B A B A
C D C D C
A B A B A
C D C D C
Each coin can never leave its class (A, B, C, or D).
As we have a coin in each class, each coin must finish
in its original position. The only tetromino with
the same distribution of class is the 2-square.
Hint2:
- Try to reverse all coins in four moves for the configuration:
. . . .
. o o .
. o o .
. . . .
Hint3:
- Conjugate the 2-square solution to solve the original problem.