The little affair of the "Runaway Motor-car" is a good illustration of
how a knowledge of some branch of puzzledom may be put to unexpected use.
A member of the Club, whose name I have at the moment of writing
forgotten, came in one night and said that a friend of his was bicycling
in Surrey on the previous day, when a motor-car came from behind, round a
corner, at a terrific speed, caught one of his wheels, and sent him
flying in the road. He was badly knocked about, and fractured his left
arm, while his machine was wrecked. The motor-car was not stopped, and he
had been unable to trace it.
There were two witnesses to the accident, which was beyond question the
fault of the driver of the car. An old woman, a Mrs. Wadey, saw the whole
thing, and tried to take the number of the car. She was positive as to
the letters, which need not be given, and was certain also that the first
figure was a 1. The other figures she failed to read on account of the
speed and dust.
The other witness was the village simpleton, who just escapes being an
arithmetical genius, but is excessively stupid in everything else.
He is always working out sums in his head; and all he could say was that
there were five figures in the number, and that he found that when he
multiplied the first two figures by the last three they made the same
figures, only in different order--just as 24 multiplied by 651 makes
15,624 (the same five figures), in which case the number of the car would
have been 24,651; and he knew there was no 0 in the number.
"It will be easy enough to find that car," said Russell. "The known facts
are possibly sufficient to enable one to discover the exact number. You
see, there must be a limit to the five-figure numbers having the
peculiarity observed by the simpleton. And these are further limited by
the fact that, as Mrs. Wadey states, the number began with the figure 1.
We have therefore to find these numbers. It may conceivably happen that
there is only one such number, in which case the thing is solved. But
even if there are several cases, the owner of the actual car may easily
be found.
"How will you manage that?" somebody asked.
"Surely," replied Russell, "the method is quite obvious. By the process
of elimination. Every owner except the one in fault will be able to prove
an alibi. Yet, merely guessing offhand, I think it quite probable that
there is only one number that fits the case. We shall see."
[Illustration]
Russell was right, for that very night he sent the number by post, with
the result that the runaway car was at once traced, and its owner, who
was himself driving, had to pay the cost of the damages resulting from
his carelessness. What was the number of the car?