A NEW COUNTER PUZZLE.
(
The Guarded Chessboard)
Here is a new puzzle with moving counters, or coins, that at first
glance looks as if it must be absurdly simple. But it will be found
quite a little perplexity. I give it in this place for a reason that I
will explain when we come to the next puzzle. Copy the simple diagram,
enlarged, on a sheet of paper; then place two white counters on the
points 1 and 2, and two red counters on 9 and 10, The puzzle is to make
the red and white change places. You may move the counters one at a time
in any order you like, along the lines from point to point, with the
only restriction that a red and a white counter may never stand at once
on the same straight line. Thus the first move can only be from 1 or 2
to 3, or from 9 or 10 to 7.
[Illustration:
4 8
/ /
2 6 10
/ /
3 7
/ /
1 5 9
]
Answer:
Play as follows: 2--3, 9--4, 10--7, 3--8, 4--2, 7--5, 8--6, 5--10, 6--9,
2--5, 1--6, 6--4, 5--3, 10--8, 4--7, 3--2, 8--1, 7--10. The white
counters have now changed places with the red ones, in eighteen moves,
without breaking the conditions.
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