What number, if divided by 10, leaves a remainder of 9; then divided by 9 leaves a remainder of 8; divided...
arithmetic/remainder.one.less New
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Problem
What number, if divided by 10, leaves a remainder of 9; then divided by 9 leaves a remainder of 8; divided by 8 leaves a remainder of 7; ... etc. ..., divided by 2 leaves a remainder of 1? One answer is 14,622,042,959. Find a smaller solution!
Show solution
The number one greater than the one you want is evenly divisible by 10, 9, 8, 7, 6, 5, 4, 3, and 2. Then 10!-1 is one solution to the puzzle, but you can get smaller yet. We simply need 3 factors of 2, two factors of 3, and one each of 5 and 7. 8*9*5*7=2520, so 2519 has the desired property. (as well as any 2520k+2519 for k=1, 2, 3, ...) -- Joseph W. DeVincentis <devjoe@wilma.che.utexas.edu>