I have nine counters, each bearing one of the nine
digits, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
I arranged them on the table in
two groups, as shown in the illustration, so as to form two
multiplication sums, and found that both sums gave the same product.
You will find that 158 multiplied by 23 is 3,634, and that 79
multiplied by 46 is also 3,634.
Now, the puzzle I propose is to
rearrange the counters so as to get as large a product as possible.
What is the best way of placing them?
Remember both groups must
multiply to the same amount, and there must be three counters
multiplied by two in one case, and two multiplied by two counters in
the other, just as at present.