In this case a certain amount of mere "trial" is unavoidable. But there
are two kinds of "trials"--those that are purely haphazard, and those
that are methodical. The true puzzle lover is never satisfied with mere
haphazard trials. The reader will find that by just reversing the
figures in 23 and 46 (making the multipliers 32 and 64) both products
will be 5,056. This is an improvement, but it is not the correct answer.
We can get as large a product as 5,568 if we multiply 174 by 32 and 96
by 58, but this solution is not to be found without the exercise of some
judgment and patience.