Squares of Sums of Digits

In this Puzzlet, SD(i) means "the sum of
the digits of i." Take an integer i and find i ^{2}, SD(i), SD(i) and [SD(i)]^{2}^{2}.By a suitable selection of i, you'll have SD(i ^{2}) = [SD(i)]^{2}^{}.Example: let i = 13, so that i ^{2} = 169, and SD(i^{2}) = 16.Also, SD(i) = 4 and [SD(i ^{})]^{2} = 16.As required, [SD(i)] ^{2 }= SD(i^{2}).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 ... |

Site design/maintenance: Dave EllisE-mail me!

Last Updated: January 21st, 2010.