DAY 232

LEFTOVERS AGAIN?
Credit: GAMES Magazine
June, 1984
Michael W. Ecker

What is the smallest whole number that, when divided by 2 leaves a remainder of 1; when divided by 3, leaves a remainder of 2; and so on, and when divided by 10 leaves a remainder of 9?

Answer:

2,519...............Since the remainder is always 1 less than the divisor, it follows that the answer must be 1 less than a multiple of all the divisors 2 through 10. The smallest such number must be the Least Common Multiple of 2, 3, 4, ...........9, 10 minus 1. The LCM is 2,520, so the answer is 2, 519.