Substitute each of the capital letters in bold by a different base ten digit from 0 to 9, such that:

• THAT is a perfect square, and none of T and I is zero, and:
• The base ten representation of the product (THIS)*(THAT)*(IT) has no leading zeroes and contains each of the digits from 0 to 9 exactly once.

I found the only solution of

 5693* 5625* 95= 3042196875
 with 5625=75^2

with the following code

CLS 0
DIM dcnt(0 TO 9)
FOR t = 1 TO 9
 FOR h = 0 TO 9
  IF h <> t THEN
   FOR a = 0 TO 9
    IF a <> t AND a <> h THEN
     FOR i = 1 TO 9
      IF i <> t AND i <> h AND i <> a THEN
       FOR s = 0 TO 9
        IF s <> t AND s <> h AND s <> a AND s <> i THEN
         this# = s + 10 * i + 100 * h + 1000 * t
         that# = t + 10 * a + 100 * h + 1000 * t
         it# = t + 10 * i
         num# = this# * that# * it#
         IF INT(SQR(that#)) = SQR(that#) THEN
          FOR j = 0 TO 9
           dcnt(j) = 0
          NEXT j
          fail = 0
          num2# = num#
          FOR j = 1 TO 10
           digit# = num2# - 10 * INT(num2# / 10)
           IF dcnt(digit#) = 1 THEN
            fail = 1
           END IF
           dcnt(digit#) = 1
           num2# = (num2# - digit#) / 10
          NEXT j
          IF fail = 0 AND digit# <> 0 THEN
           PRINT STR$(this#) + "*" + STR$(that#) + "*" + STR$(it#) + "=" + STR$(num#)
           PRINT STR$(SQR(that#)) + "^2 = " + STR$(that#)
          END IF
         END IF
        END IF
       NEXT s
      END IF
     NEXT i
    END IF
   NEXT a
  END IF
 NEXT h
NEXT t

 

Posted by Daniel on 2009-06-19 12:55:27