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The Egg Seller's Problem

Unreviewed import — a classic from the public domain; its solution has not been machine-checked yet.

math
A woman carrying a basket of eggs is bumped into and drops the basket, breaking all the eggs. When asked how many eggs she had, she replies that she doesn’t know for sure, but she remembers that when counted two by two, one egg remained; similarly, when counted three by three, four by four, five by five, or even six by six, one egg remained each time. However, when counted seven by seven, none remained. What is the total number of eggs she had?

Solution

Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.

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