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 A quotation (Posted on 2014-01-07)
The following alphametic summation puzzle:

WORDS
+WORDS
+WORDS
-----------
AVOWED

has a unique solution in base 10.

Find it.

Is there a solution in base 8?

 See The Solution Submitted by Ady TZIDON No Rating

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 computer solution | Comment 1 of 2

DECLARE SUB permute (a\$)
CLS
a\$ = "1234567890": h\$ = a\$
DO
IF INSTR(a\$, "0") > 2 THEN
w = VAL(MID\$(a\$, 1, 1))
a = VAL(MID\$(a\$, 2, 1))
o = VAL(MID\$(a\$, 3, 1))
r = VAL(MID\$(a\$, 4, 1))
d = VAL(MID\$(a\$, 5, 1))
s = VAL(MID\$(a\$, 6, 1))
v = VAL(MID\$(a\$, 7, 1))
e = VAL(MID\$(a\$, 8, 1))
END IF
words = 10000 * w + 1000 * o + 100 * r + 10 * d + s
avowed = 100000 * a + 10000 * v + 1000 * o + 100 * w + 10 * e + d
IF 3 * words = avowed THEN
PRINT words, avowed
END IF
permute a\$
LOOP UNTIL a\$ = h\$
a\$ = "12345670": h\$ = a\$
DO
IF INSTR(a\$, "0") > 2 THEN
w = VAL(MID\$(a\$, 1, 1))
a = VAL(MID\$(a\$, 2, 1))
o = VAL(MID\$(a\$, 3, 1))
r = VAL(MID\$(a\$, 4, 1))
d = VAL(MID\$(a\$, 5, 1))
s = VAL(MID\$(a\$, 6, 1))
v = VAL(MID\$(a\$, 7, 1))
e = VAL(MID\$(a\$, 8, 1))
END IF
words = 8 * 8 * 8 * 8 * w + 8 * 8 * 8 * o + 8 * 8 * r + 8 * d + s
avowed = 8 * 8 * 8 * 8 * 8 * a + 8 * 8 * 8 * 8 * v + 8 * 8 * 8 * o + 8 * 8 * w + 8 * e + d
IF 3 * words = avowed THEN
PRINT words, avowed
END IF
permute a\$
LOOP UNTIL a\$ = h\$

finds

34786         104358

for WORDS and AVOWED respectively in base 10.

None are found for base 8.

 Posted by Charlie on 2014-01-07 18:05:03

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