Eggs and Meteorite
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 them by 3's, there was 1 left over;
when he counted them by 4's, there was 1 left over;
when he counted them by 5's, there was 1 left over;
when he counted them by 6's, there was 1 left over;
but when he counted them by 7's, there were none left over.
What is the smallest number of eggs that were in the truck?
The answer is 301.
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LCM of (2,3,4,5,6)=60
The required number is (60.x +1)%7=0.
x=5, which is the minimum value satisfying the above equation 301%7=0.
So the required result is 301.