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 one, two, six, mod alphametics (Posted on 2008-11-30)
Substitute each of the small letters in bold with a different decimal digit from 0 to 9, to satisfy the following system of simultaneous modular alphametic equations:

one ≡ 1 (mod two), and:
one ≡ 1 (mod six), and:
six ≡ 0 (mod two)

where, none of s, o and t is zero.

Note: Try to derive a non computer-assisted solution, although computer program/spreadsheet solutions are welcome.

 See The Solution Submitted by K Sengupta No Rating

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 computer solution Comment 2 of 2 |

PRINT

FOR o = 1 TO 9
IF used(o) = 0 THEN
used(o) = 1
FOR n = 0 TO 9
IF used(n) = 0 THEN
used(n) = 1
FOR e = 0 TO 9
IF used(e) = 0 THEN
used(e) = 1
one = o * 100 + n * 10 + e
FOR t = 1 TO 9
IF used(t) = 0 THEN
used(t) = 1
FOR w = 0 TO 9
IF used(w) = 0 THEN
used(w) = 1
two = t * 100 + w * 10 + o
IF one MOD two = 1 THEN
FOR s = 1 TO 9
IF used(s) = 0 THEN
used(s) = 1
FOR i = 0 TO 9
IF used(i) = 0 THEN
used(i) = 1
FOR x = 0 TO 9
IF used(x) = 0 THEN
used(x) = 1

six = s * 100 + i * 10 + x
IF six MOD two = 0 AND one MOD six = 1 THEN
PRINT one; two; six
END IF

used(x) = 0
END IF
NEXT
used(i) = 0
END IF
NEXT
used(s) = 0
END IF
NEXT
END IF
used(w) = 0
END IF
NEXT
used(t) = 0
END IF
NEXT
used(e) = 0
END IF
NEXT
used(n) = 0
END IF
NEXT
used(o) = 0
END IF
NEXT

produces

865  108  432

indicating one, two and six in that order.

 Posted by Charlie on 2008-11-30 21:44:26

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