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PUZZLET 201

Squares of Sums of Digits

In this Puzzlet, SD(i) means "the sum of the digits of i."

Take an integer i and find i2, SD(i), SD(i
2) and [SD(i)]
2.
By a suitable selection of i, you'll have
SD(i2) = [SD(i)]2.

Example: let i = 13, so that i2 = 169, and SD(i2) = 16.
Also, SD(i) = 4 and [SD(i)]2 = 16.
As required, [SD(i)]2 = SD(i2).

The challenge is to find the smallest solutions for which SD(i) = 1 up to SD(i) = 7.  You already have the solution for SD(i) = 4, and the solutions for SD(i) = 1 to 3 are trivial, so you should be well on your way ...



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Last Updated: January 21st, 2010.