Broken Eggs
An egg trader was moving along a road selling eggs. An idler who didn't have much work to do started to get the egg trader into a wordy duel. This grew into a fight and he pulled the basket with eggs and dashed it on the floor. The eggs broke.
The trader requested the Panchayat (five member committee) meeting to settle the dispute. The Panchayat asked the trader how many eggs were broken ? He gave the following response
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I had less than 150 eggs.
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If you count in pairs, one will remain
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If you count in a group of three, two will remain
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If you count in a group of four, three will remain
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If you count in a group of five, four will remain
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If you count in a group of six, five will remain
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If you count in a group of seven, nothing will remain.
How many eggs do you think have been broken?
The answer is 119.
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1 solution
When he eggs are counted in pairs, or groups of three, an egg or two remains:
As we know the number of eggs is less than 150.
We can use modulous to find the number of eggs:
Therefore the number of eggs is 1 1 9 .