Going Bananas

You feel a tug at your sleeve. It is another merchant.

“You have a formidable talent, my friend,” he remarks. “Can I interest you in a small problem? Your answer to it is worth three obols to me.”

“What is it?” you ask.

Three of my traders had purchased a load of bananas—between 50 and 100—for me, but got lost in the mountains one night. The bananas were all that could keep them alive, and they agreed to divide them into equal portions the next morning.

It turns out that each man was worried about receiving his share and so awoke in the night to claim a portion. Each, unbeknownst to the others, took one-third of the bananas and hid them for future consumption.

Curiously enough, each man found that the bananas divided into even thirds—with one left over. They each gave the leftover banana to a friendly mountain goat and went back to sleep.

In the morning, they divided the stack again into thirds, again with one banana left over for the goat, and waited to be rescued.

Eventually they were rescued—after having to admit to their secret stashes and eat all the bananas. But none can remember how many bananas there were or how many they ate.

I must know how many bananas I lost if I am to correctly figure my gains and losses for this quarter. Can you help me?

Solve the merchant’s quandary by emailing <public at etgdesign dot com> …

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