Let
m*n=w (i)
m is a 3digit number
so is n
w is a 6digit number
In equation (i) only 4 distinct digits are used.
Find the possible equations.
A quick look at some perfect squares yields some easy ones.
Repdigits
666*666=443556
888*888=788554
999*999=998001
there are many ending in 1 or 2 zeros, for example:
800*800=640000
630*630=390900
also, many ending in 1, 5 or 6 since the square will too:
501*501=251001
715*715=511225
more interesting then are some sporadic ones:
369*369=136161
472*472=222784
642*642=412514
I like these 3 in a row:
525*525=275625
526*526=276676
527*527=277729
Some nonperfect square examples that use zeros at the end are a bit of a cheat:
200*600=120000
500*800=400000
500*900=450000
I'm sure a computer solution will turn up dozens more if not hundreds.

Posted by Jer
on 20171203 10:24:46 