In the following equation, each of the x’s as well as each of W, A and Y represents a decimal digit from 0 to 9 whether same or different. None of the numbers can contain any leading zero.

(WAY)*(WAY) = (xxxxxxWAY)/1983

What are the respective minimum value and the maximum value of WAY?

DEFDBL A-Z

FOR w = 1 TO 9
FOR a = 0 TO 9
  FOR y = 0 TO 9
    way = w * 100 + a * 10 + y
    prod = way * way * 1983
    IF prod MOD 1000 = way THEN
      IF prod > 100000000 AND prod < 1000000000 THEN
        PRINT way, prod
      END IF
    END IF
  NEXT
NEXT
NEXT

 272           146710272
 375           278859375
 647           830101647

 

Posted by Charlie on 2009-04-08 17:42:02