Contribution for Puzzlet #023

From: Denis Borris [borrisd@ca.inter.net]

You can do that with 3 lines of code only, doing only 9 calculations.

You say to derive a formula, then use computer, so:

Let x = abcde; then fabcde = f*abcdef becomes:

10^5 * f + x = f * (10*x + f)

simplify to get:

x = (f * (10^5 - f)) / (10 * f - 1)

So now we only need to loop f from 1 to 9.

My Ubasic code:

For f = 1 to 9

Print (f * (10^5 - f)) / (10 * f - 1)

Next f

Out of 9, 2 integer results will appear:

f=1: 11111

f=4: 10256

Thanks, Denis. I had originally dismissed the "trivial" solution of 11111, but you're right to point it out - it's a

valid answer. Dave.

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