I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!

Thursday, March 23, 2006

Smallest Integer

What is the smallest positive integer that leaves a remainder of 1 when divided by 2, remainder of 2 when divided by 3, a remainder of 3 when divided by 4, … and a remainder of 9 when divided by 10?

Answer is 2519.... As all the numbers leave a remainder which is one less than the number i.e, 8 leaves 7, 6 leaves 5 etc ... which suggests that the unknown number +1 should be divisible by all the numbers..... and hence taking the Least Common Multiple of numbers from 2 through 9 which is 2520 is the first possible number which is divisible by all the numbers and so answer would be 2520-1=2519

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Answer is 2519....

ReplyDeleteAs all the numbers leave a remainder which is one less than the number i.e, 8 leaves 7, 6 leaves 5 etc ... which suggests that the unknown number +1 should be divisible by all the numbers..... and hence taking the Least Common Multiple of numbers from 2 through 9 which is 2520 is the first possible number which is divisible by all the numbers and so answer would be 2520-1=2519