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."

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?

See answer