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 base1000.

Posted by Charlie
on 20070828 15:12:04 