Solution to What Did You Do Last Summer?

To summarize the problem, what single number when divided by the number in the left column has a remainder as shown in the right column?

Divisor Remainder
------- ---------
   2       1
   3       2
   4       3
   5       4
   6       5
   7       6
   8       7
   9       8

If you didn't get the solution within five minutes don't feel bad, I don't know anyone who's been that quick. And if you couldn't figure it out, you've got a fair amount of company.

The number of pennies is 2519.

How do you get the answer?

To me, this is a two part problem. First you have to recognize when a division problem has a remainder that is 1 less than the divisor. This happens any time the dividend is 1 less than any integer multiple (greater than 1) of the divisor:

        (D*N) - 1
        ------------
             D

        for     N = 2, 3, 4, ...

The second part is the need to find the least common multiple of 2, 3, 4, 5, 6, 7, 8, and 9. This is (2^3)(3^2)(5)(7) or 2520.

So the answer is 2520 - 1, or 2519.

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