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 Going Arithmetic With Alphametic II (Posted on 2009-11-21)
Substitute each of the capital letters in bold by a different digit from 0 to 9 such that the sum of digits of each of POIRE, OPERA, PORTE, TAPIS, ASTRE, PATRE, LOTUS, LISTE, LOUPE and, OUTRE (in this order) constitutes ten consecutive terms of an arithmetic sequence in ascending order. It is known that none of P, O, T, A and L can be zero.

 See The Solution Submitted by K Sengupta No Rating

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 computer solution | Comment 1 of 3

DIM used(-100 TO 100)
FOR k = 0 TO 9
FOR a = 1 TO 9
used(a) = 1
i = a - k
IF used(i) = 0 AND i >= 0 AND i < 10 THEN
used(i) = 1
t = a + k
IF used(t) = 0 AND t > 0 AND t < 10 THEN
used(t) = 1
FOR p = 1 TO 9
IF used(p) = 0 THEN
used(p) = 1
s = p - k
IF used(s) = 0 AND s >= 0 AND s < 10 THEN
used(s) = 1
FOR r = 0 TO 9
IF used(r) = 0 THEN
used(r) = 1
e = p + a - r
IF used(e) = 0 AND e >= 0 AND e < 10 THEN
used(e) = 1
IF p + e = t + s + 2 * k THEN

l = t + r - p - k
IF used(l) = 0 AND l > 0 AND l < 10 THEN
used(l) = 1

o = 2 * i + s - r - e
IF used(o) = 0 AND o > 0 AND o < 10 THEN
used(o) = 1

u = i + e - o - k
IF used(u) = 0 AND u >= 0 AND u < 10 THEN
used(u) = 1
GOSUB printIt
used(u) = 0
END IF

used(o) = 0
END IF

used(l) = 0
END IF

END IF
used(e) = 0
END IF
used(r) = 0
END IF
NEXT r
used(s) = 0
END IF
used(p) = 0
END IF
NEXT p
used(t) = 0
END IF
used(i) = 0
END IF
used(a) = 0
NEXT a
NEXT k

END
printIt:
PRINT "poire", p; o; i; r; e, p + o + i + r + e
PRINT "opera", o; p; e; r; a, o + p + e + r + a
PRINT "porte", p; o; r; t; e, p + o + r + t + e
PRINT "tapis", t; a; p; i; s, t + a + p + i + s
PRINT "astre", a; s; t; r; e, a + s + t + r + e
PRINT "patre", p; a; t; r; e, p + a + t + r + e
PRINT "lotus", l; o; t; u; s, l + o + t + u + s
PRINT "liste", l; i; s; t; e, l + i + s + t + e
PRINT "loupe", l; o; u; p; e, l + o + u + p + e
PRINT "outre", o; u; t; r; e, o + u + t + r + e
RETURN

finds

`word               digits                s.o.d.poire          2  3  5  0  8               18opera          3  2  8  0  6               19porte          2  3  0  7  8               20tapis          7  6  2  5  1               21astre          6  1  7  0  8               22patre          2  6  7  0  8               23lotus          4  3  7  9  1               24liste          4  5  1  7  8               25loupe          4  3  9  2  8               26outre          3  9  7  0  8               27`

 Posted by Charlie on 2009-11-21 15:13:53

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