In this 4x4 grid, each of the capital letters in bold represents a different base ten digit from 0 to 9, such that the sum of each of the four columns as well as the sum of each of the four rows is ET.

E   L   M   S
R   E   I   N
A   N  T   I
S   T   E   P

Determine the respective minimum value and the maximum value of ET.

Note: ET is equal to 10*E+ T.

1 2 9 4
8 1 0 7
3 7 6 0
4 6 1 5
16      1 6

1 9 2 4
8 1 7 0
3 0 6 7
4 6 1 5
16      1 6

1 3 9 2
8 1 0 6
4 6 5 0
2 5 1 7
15      1 5

1 9 3 2
8 1 6 0
4 0 5 6
2 5 1 7
15      1 5

1 6 7 0
8 1 2 3
5 3 4 2
0 4 1 9
14      1 4

1 7 6 0
8 1 3 2
5 2 4 3
0 4 1 9
14      1 4

totals of 14 through 16.

Only if E had been zero would there be a problem, for ET.

CLS

FOR e = 0 TO 9
 IF used(e) = 0 THEN
  used(e) = 1
FOR r = 0 TO 9
 IF used(r) = 0 THEN
  used(r) = 1
FOR a = 0 TO 9
 IF used(a) = 0 THEN
  used(a) = 1
FOR s = 0 TO 9
 IF used(s) = 0 THEN
  used(s) = 1
FOR l = 0 TO 9
 IF used(l) = 0 THEN
  used(l) = 1
FOR n = 0 TO 9
 IF used(n) = 0 THEN
  used(n) = 1
FOR t = 0 TO 9
 IF used(t) = 0 THEN
  used(t) = 1
FOR m = 0 TO 9
 IF used(m) = 0 THEN
  used(m) = 1
FOR i = 0 TO 9
 IF used(i) = 0 THEN
  used(i) = 1
FOR p = 0 TO 9
 IF used(p) = 0 THEN
  used(p) = 1

  s1 = e + l + m + s
  s2 = r + e + i + n
  s3 = a + n + t + i
  s4 = s + t + e + p
  s5 = e + r + a + s
  s6 = l + e + n + t
  s7 = m + i + t + e
  s8 = s + n + i + p
  IF s1 = 10 * e + t AND s1 = s2 AND s2 = s3 AND s3 = s4 THEN
    IF s4 = s5 AND s5 = s6 AND s6 = s7 AND s7 = s8 THEN
      PRINT e; l; m; s
      PRINT r; e; i; n
      PRINT a; n; t; i
      PRINT s; t; e; p
      PRINT s1, e; t: PRINT
    END IF
  END IF

  used(p) = 0
 END IF
NEXT
  used(i) = 0
 END IF
NEXT
  used(m) = 0
 END IF
NEXT
  used(t) = 0
 END IF
NEXT
  used(n) = 0
 END IF
NEXT
  used(l) = 0
 END IF
NEXT
  used(s) = 0
 END IF
NEXT
  used(a) = 0
 END IF
NEXT
  used(r) = 0
 END IF
NEXT
  used(e) = 0
 END IF
NEXT

 

Posted by Charlie on 2009-07-31 17:16:22