## Fun with Chinese Remainder Theorem

A farmer is on the way to market to sell eggs when a meteorite hits his truck and destroys all of his produce. In order to file an insurance claim, he needs to know how many eggs were broken. He knows that when he counted the eggs by 2’s, there was 1 left over, when he counted the eggs by 3’s, there was 1 left over, when he counted the eggs by 4’s, there was 1 left over,

when he counted the eggs by 5’s, there was 1 left over, and when he counted them by 6’s, there was one left over, but when he counted them by 7’s, there was none left over. What is the smallest number of eggs that were in the truck?

More fun later…

Nalin Pithwa

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## 3 Comments

My first guess is 91

Remainder when 91 is divided by 4 is 3. So 91 is not the right answer.

My second guess is 301