A number and its square both have the same last three digits. What are the possibilities for those digits?

(In reply to Solution (not necessarily a full list) by Guest)

000
001
376
625

is indeed the full list, found by

FOR i = 0 TO 999
    sq = i * i
    d$ = "000" + LTRIM$(STR$(sq))
    n = VAL(RIGHT$(d$, 3))
    IF i = n THEN PRINT RIGHT$(d$, 3)
NEXT

That digits further to the left than the hundreds position could interfere is not a possibility, as one could consider the numbers in base 1000. When squaring a number in any base system, or any multiplication in any base system, multiplying the rightmost digits always results in the rightmost digit of the answer, including base-1000.

Posted by Charlie on 2007-08-28 15:12:04