The children in the illustration have found that a large number of very
interesting and instructive puzzles may be made out of number blocks;
that is, blocks bearing the ten digits or Arabic figures--1, 2, 3, 4, 5,
6, 7, 8, 9, and 0. The particular puzzle that they have been amusing
themselves with is to divide the blocks into two groups of five, and then
so arrange them in the form of two multiplication sums that one product
shall be the same as the other. The number of possible solutions is very
considerable, but they have hit on that arrangement that gives the
smallest possible product. Thus, 3,485 multiplied by 2 is 6,970, and
6,970 multiplied by 1 is the same. You will find it quite impossible to
get any smaller result.
[Illustration]
Now, my puzzle is to find the largest possible result. Divide the blocks
into any two groups of five that you like, and arrange them to form two
multiplication sums that shall produce the same product and the largest
amount possible. That is all, and yet it is a nut that requires some
cracking. Of course, fractions are not allowed, nor any tricks whatever.
The puzzle is quite interesting enough in the simple form in which I have
given it. Perhaps it should be added that the multipliers may contain two
figures.