(related to Problem: The Nine Counters)
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.
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