Balls and Baskets
We have a number of Balls
if we divide Balls equally on 2 Baskets, there will be 1 Ball left.
if we divide Balls equally on 3 Baskets,there will be 1 Ball left.
if we divide Balls equally on 4 Baskets, there will be 1 Ball left.
if we divide Balls equally on 5 Baskets, there will be 1 Ball left.
if we divide Balls equally on 6 Baskets, there will be 1 ball left.
if we divide Balls equally on 7 Baskets, there will be no balls left.
What is the least possible number of Balls?
Image Credit: Flickr Sameer Vasta .
The answer is 301.
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1 solution
Taking the LCM of 2 , 3 , 4 , 5 , 6 and letting the least number be x , we see that the following two congruences must hold.
x ≡ 1 (mod 60)
x ≡ 0 (mod 7)
Using Chinese Remainder Theorem, you get that x = 3 0 1