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 Simultaneous Settlement III (Posted on 2013-12-27)
Solve this set of simultaneous alphametic equations, where HUIT and NEUF are respectively positive integers in base 8 and base 9 notation. Each of the letters in bold represents a different digit, and none of the numbers contains any leading zero.

(HUIT)8 = (NEUF)9 - 1, and:
sod(HUIT) = sod(NEUF) - 1

Extra Challenge: A non computer program aided solution.

*** sod(x) denotes the numeric value of the sum of the digits of x.

 No Solution Yet Submitted by K Sengupta No Rating

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 solution without extra challenge (spoiler) Comment 1 of 1

FOR h = 1 TO 7
used(h) = 1
FOR u = 0 TO 7
IF used(u) = 0 THEN
used(u) = 1
FOR i = 0 TO 7
IF used(i) = 0 THEN
used(i) = 1
FOR t = 0 TO 7
IF used(t) = 0 THEN
used(t) = 1
sod1 = h + u + i + t
huit = t + 8 * (i + 8 * (u + 8 * h))
FOR n = 1 TO 8
IF used(n) = 0 THEN
used(n) = 1
FOR e = 0 TO 8
IF used(e) = 0 THEN
used(e) = 1
FOR f = 0 TO 8
IF used(f) = 0 THEN
used(f) = 1
sod2 = n + e + u + f
neuf = f + 9 * (u + 9 * (e + 9 * n))
IF huit = neuf - 1 AND sod1 = sod2 - 1 THEN
PRINT h; u; i; t, n; e; u; f, huit, neuf
END IF
used(f) = 0
END IF
NEXT
used(e) = 0
END IF
NEXT
used(n) = 0
END IF
NEXT
used(t) = 0
END IF
NEXT
used(i) = 0
END IF
NEXT
used(u) = 0
END IF
NEXT
used(h) = 0
NEXT

finds

`                                   as                                 decimalH  U  I  T    N  E  U  F    huit          neuf                            value         value`
`5  4  7  0    3  8  4  2    2872          2873`

 Posted by Charlie on 2013-12-27 17:29:39

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