Alfonso has forgotten the password of his safe. However he remembers that:

1. The number is a ten digit positive integer using each of the digits from 0 to 9 exactly once.
2. The sum of the 2nd, 5th, 6th and 8th digits is a single digit number.
3. The 4th digit is a perfect square.
4. The 3rd digit is 1
5. The sum of the 4th and 7th digits is a perfect square.
6. The value of the 10th digit is twice that of the 2nd digit.
7. The product of the 4th digit and the 6th digit is equal to that of the 2nd digit and the 10th digit.
8. 5 is next to 6 but not 4.

From the above clues, can you help Alfonso to crack the password to open the safe?

DECLARE SUB permute (a$)
CLS
a0$ = "234567890": h$ = a0$
DO
  a$ = LEFT$(a0$, 2) + "1" + MID$(a0$, 3)
  d1 = VAL(MID$(a$, 1, 1))
  d2 = VAL(MID$(a$, 2, 1))
  d3 = VAL(MID$(a$, 3, 1))
  d4 = VAL(MID$(a$, 4, 1))
  d5 = VAL(MID$(a$, 5, 1))
  d6 = VAL(MID$(a$, 6, 1))
  d7 = VAL(MID$(a$, 7, 1))
  d8 = VAL(MID$(a$, 8, 1))
  d9 = VAL(MID$(a$, 9, 1))
  d10 = VAL(MID$(a$, 10, 1))
  IF d2 + d5 + d6 + d8 < 10 THEN
    IF d4 = 0 OR d4 = 1 OR d4 = 4 OR d4 = 9 THEN
      sq = d4 + d7
      sr = INT(SQR(sq) + .5)
      IF sr * sr = sq THEN
        IF d10 = 2 * d2 THEN
          IF d4 * d6 = d2 * d10 THEN
            IF INSTR(a$, "56") > 0 OR INSTR(a$, "65") > 0 THEN
            IF INSTR(a$, "54") = 0 AND INSTR(a$, "45") = 0 THEN
               PRINT a$
            END IF
            END IF
          END IF
        END IF
      END IF
    END IF
  END IF
  permute a0$
LOOP UNTIL a0$ = h$

finds

8319427056

Posted by Charlie on 2014-03-17 12:06:55