### Brain Teasers

# How Many Eggs

Once upon a time, an old lady went to sell her vast quantity of eggs at the local market.

When asked how many she had, she replied:

Son, I can't count past 100 but I know that -

If you divide the number of eggs by 2 there will be one egg left.

If you divide the number of eggs by 3 there will be one egg left.

If you divide the number of eggs by 4 there will be one egg left.

If you divide the number of eggs by 5 there will be one egg left.

If you divide the number of eggs by 6 there will be one egg left.

If you divide the number of eggs by 7 there will be one egg left.

If you divide the number of eggs by 8 there will be one egg left.

If you divide the number of eggs by 9 there will be one egg left.

If you divide the number of eggs by 10 there will be one egg left.

Finally, if you divide the number of eggs by 11 there will be NO EGGS left!

What's the minimum number of eggs that the old lady could have?

When asked how many she had, she replied:

Son, I can't count past 100 but I know that -

If you divide the number of eggs by 2 there will be one egg left.

If you divide the number of eggs by 3 there will be one egg left.

If you divide the number of eggs by 4 there will be one egg left.

If you divide the number of eggs by 5 there will be one egg left.

If you divide the number of eggs by 6 there will be one egg left.

If you divide the number of eggs by 7 there will be one egg left.

If you divide the number of eggs by 8 there will be one egg left.

If you divide the number of eggs by 9 there will be one egg left.

If you divide the number of eggs by 10 there will be one egg left.

Finally, if you divide the number of eggs by 11 there will be NO EGGS left!

What's the minimum number of eggs that the old lady could have?

### Hint

Recall that if n is a prime number, (n-1)!+1 is divisible by n.### Answer

10!+1=3628801 eggs. This is an answer, but not the minimum.The least common multiple of 1 to 11 is 27720.

3628801=27720*130+25201.

Therefore, the old lady had at least 25201 eggs.

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