Nine counters, each bearing one of
the nine digits from 1 through 9, are arranged in two groups as is
shown. Each group represents a multiplication and, more interestingly,
results in the same product. As it can be seen 158 multiplied by 23 is
the same as 79 multiplied by 46 which gives 3,634 in both cases.
The challenge is to rearrange the counters so that to get as large
product as possible. Remember both groups must multiply to the same
amount, and there must be three counters multiplied by two in one
group, and two multiplied by two counters in the other, just as it is
now. What is the biggest amount which can be produced?