Grandma's Eggs
While I was visiting my grandma, I remembered that she had gotten a whole plantation of chickens and was now selling eggs by the crate. Out of curiosity, I asked her how many eggs she sold. She replied,
"I certainly can't count that high, but I know that if you divide the number of eggs by each integer from {2, 3, 4, ..., 10}, then you will have one egg leftover. However, if you divide the number of eggs by 11, there is no remainder!"
"Thank you, Grandma! Now, did you sell less than 30,000 eggs?"
"Why, yes, I believe I did!"
How many eggs did Grandma sell?
The answer is 25201.
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1 solution
LCM of (2,3,4,5,6,7,8,9,10)=2520
The required number is (2520.x +1)%11=0.
x=10 which is the minimum value satisfying the above equation 25201%11=0.
So the required result is 25201.