THE VICTORIA CROSS PUZZLE.
(
Moving Counter Problem)
[Illustration:
+---------------------+
| ... A .../ |
| (I) |.......| (V) |
|_____|_______|_____/|
|......| |------|
|.. R .| |. I ..|
|......| |......|
| _____|_______|_____ |
|/ |.......| |
| (O) |.. T ..| (C) |
| /......... |
+---------------------+
]
The puzzle-maker is peculiarly a "snapper-up of unconsidered trifles,"
and his productions are often built up with the slenderest materials.
Trivialities that might entirely escape the observation of others, or,
if they were observed, would be regarded as of no possible moment, often
supply the man who is in quest of posers with a pretty theme or an idea
that he thinks possesses some "basal value."
When seated opposite to a lady in a railway carriage at the time of
Queen Victoria's Diamond Jubilee, my attention was attracted to a brooch
that she was wearing. It was in the form of a Maltese or Victoria Cross,
and bore the letters of the word VICTORIA. The number and arrangement of
the letters immediately gave me the suggestion for the puzzle which I
now present.
The diagram, it will be seen, is composed of nine divisions. The puzzle
is to place eight counters, bearing the letters of the word VICTORIA,
exactly in the manner shown, and then slide one letter at a time from
black to white and white to black alternately, until the word reads
round in the same direction, only with the initial letter V on one of
the black arms of the cross. At no time may two letters be in the same
division. It is required to find the shortest method.
Leaping moves are, of course, not permitted. The first move must
obviously be made with A, I, T, or R. Supposing you move T to the
centre, the next counter played will be O or C, since I or R cannot be
moved. There is something a little remarkable in the solution of this
puzzle which I will explain.
Answer:
In solving this puzzle there were two things to be achieved: first, so
to manipulate the counters that the word VICTORIA should read round the
cross in the same direction, only with the V on one of the dark arms;
and secondly, to perform the feat in the fewest possible moves. Now, as
a matter of fact, it would be impossible to perform the first part in
any way whatever if all the letters of the word were different; but as
there are two I's, it can be done by making these letters change
places--that is, the first I changes from the 2nd place to the 7th, and
the second I from the 7th place to the 2nd. But the point I referred to,
when introducing the puzzle, as a little remarkable is this: that a
solution in twenty-two moves is obtainable by moving the letters in the
order of the following words: "A VICTOR! A VICTOR! A VICTOR I!"
There are, however, just six solutions in eighteen moves, and the
following is one of them: I (1), V, A, I (2), R, O, T, I (1), I (2), A,
V, I (2), I (1), C, I (2), V, A, I (1). The first and second I in the
word are distinguished by the numbers 1 and 2.
It will be noticed that in the first solution given above one of the I's
never moves, though the movements of the other letters cause it to
change its relative position. There is another peculiarity I may point
out--that there is a solution in twenty-eight moves requiring no letter
to move to the central division except the I's. I may also mention that,
in each of the solutions in eighteen moves, the letters C, T, O, R move
once only, while the second I always moves four times, the V always
being transferred to the right arm of the cross.
Informational
