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 3x3 Grid Alphamagic (Posted on 2009-09-17)
Substitute each of the capital letters by a different digit from 0 to 9, such that each of the columns, each of the rows and each of the two main diagonals of this 3x3 grid have the common sum LRK. It is known that L is nonzero and, none of the numbers in the nine cells contains a leading zero.

CL    RO    OR
EK    HS    AA
KE    KB    SH

Note: LRK is equal to 100*L + 10*R + K.

 See The Solution Submitted by K Sengupta Rating: 3.0000 (1 votes)

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 computer solution | Comment 1 of 2

31  76  67
94  58  22
49  40  85

CLS

b = 0

FOR c = 1 TO 9
IF used(c) = 0 THEN
used(c) = 1
FOR r = 1 TO 9
IF used(r) = 0 THEN
used(r) = 1
FOR o = 1 TO 9
IF used(o) = 0 THEN
used(o) = 1
ro = 10 * r + o
vor = 10 * o + r
FOR e = 1 TO 9
IF used(e) = 0 THEN
used(e) = 1
FOR h = 1 TO 9
IF used(h) = 0 THEN
used(h) = 1
FOR a = 1 TO 9
IF used(a) = 0 THEN
used(a) = 1
aa = 10 * a + a
FOR k = 1 TO 9
IF used(k) = 0 THEN
used(k) = 1
ek = 10 * e + k
ke = 10 * k + e
kb = 10 * k + b
FOR s = 1 TO 9
IF used(s) = 0 THEN
used(s) = 1
hs = 10 * h + s
sh = 10 * s + h
FOR l = 1 TO 9
IF used(l) = 0 THEN
used(l) = 1

cl = 10 * c + l
lrk = 100 * l + 10 * r + k
IF cl + ro + vor = lrk THEN
IF ek + hs + aa = lrk THEN
IF ke + kb + sh = lrk THEN
IF cl + ek + ke = lrk THEN
IF ro + hs + kb = lrk THEN
IF sh + aa + vor = lrk THEN
IF ke + hs + vor = lrk THEN
IF cl + hs + sh = lrk THEN

PRINT cl; ro; vor
PRINT ek; hs; aa
PRINT ke; kb; sh

END IF
END IF
END IF
END IF
END IF
END IF
END IF
END IF

used(l) = 0
END IF
NEXT
used(s) = 0
END IF
NEXT
used(k) = 0
END IF
NEXT
used(a) = 0
END IF
NEXT
used(h) = 0
END IF
NEXT
used(e) = 0
END IF
NEXT
used(o) = 0
END IF
NEXT
used(r) = 0
END IF
NEXT
used(c) = 0
END IF
NEXT

 Posted by Charlie on 2009-09-17 13:55:21

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