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 Near Magic Square Alphametics (Posted on 2009-07-31)
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.

 See The Solution Submitted by K Sengupta No Rating

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 computer solution | Comment 4 of 5 |
`1 2 9 48 1 0 73 7 6 04 6 1 516      1 6`
`1 9 2 48 1 7 03 0 6 74 6 1 516      1 6`
`1 3 9 28 1 0 64 6 5 02 5 1 715      1 5`
`1 9 3 28 1 6 04 0 5 62 5 1 715      1 5`
`1 6 7 08 1 2 35 3 4 20 4 1 914      1 4`
`1 7 6 08 1 3 25 2 4 30 4 1 914      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

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