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 Sum Celebrity Concerns (Posted on 2010-07-25)
Solve separately each of these base ten alphametics. None of the numbers (including those covered under functions) corresponding to any of the following alphametics can contain leading zero.

(I) THOMAS+MALTHUS+1766+1834+RR=RRRRRRR, whenever MOST is divisible by 23.

(II) DINAH+SHORE+1916+1994+TT=TTTTT, where:
sod(DEAR)/sod(HEARTS) = 2/3 and, dr(ROSE) = 4

(III) BENNY+BELL+1906+1999+BBB= DR+DE+MENTO, where:
sod(TRY)/sod(BLEND) = 4/9

Note:sod(x) denotes the sum of digits of x and dr(x) denotes the digital root of x.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution for part 1 | Comment 1 of 3

CLS
FOR t = 1 TO 9
IF used(t) = 0 THEN
used(t) = 1
FOR m = 1 TO 9
IF used(m) = 0 THEN
used(m) = 1
FOR r = 1 TO 9
IF used(r) = 0 THEN
used(r) = 1
FOR h = 0 TO 9
IF used(h) = 0 THEN
used(h) = 1
FOR o = 0 TO 9
IF used(o) = 0 THEN
used(o) = 1
FOR a = 0 TO 9
IF used(a) = 0 THEN
used(a) = 1
FOR s = 0 TO 9
IF used(s) = 0 THEN
used(s) = 1

thomas = t * 100000 + h * 10000 + o * 1000 + m * 100 + a * 10 + s
rr = r * 11
rrrrrrr = r * 1111111
malthus = rrrrrrr - rr - 1834 - 1766 - thomas
t\$ = LTRIM\$(STR\$(thomas))
m\$ = LTRIM\$(STR\$(malthus))
IF LEN(m\$) = 7 THEN
IF MID\$(t\$, 1, 1) = MID\$(m\$, 4, 1) THEN
IF MID\$(t\$, 2, 1) = MID\$(m\$, 5, 1) THEN
IF MID\$(t\$, 4, 1) = MID\$(m\$, 1, 1) THEN
IF MID\$(t\$, 5, 1) = MID\$(m\$, 2, 1) THEN
IF MID\$(t\$, 6, 1) = MID\$(m\$, 7, 1) THEN
IF used(VAL(MID\$(m\$, 3, 1))) = 0 AND used(VAL(MID\$(m\$, 6, 1))) = 0 THEN
IF MID\$(m\$, 3, 1) <> MID\$(m\$, 6, 1) THEN
most = m * 1000 + o * 100 + s * 10 + t
IF most MOD 23 = 0 THEN
PRINT thomas; malthus, r
END IF
END IF
END IF
END IF
END IF
END IF
END IF
END IF
END IF

used(s) = 0
END IF
NEXT
used(a) = 0
END IF
NEXT
used(o) = 0
END IF
NEXT
used(h) = 0
END IF
NEXT
used(r) = 0
END IF
NEXT
used(m) = 0
END IF
NEXT
used(t) = 0
END IF
NEXT

finds

`THOMAS  MALTHUS             R840135  1378465             2`

 Posted by Charlie on 2010-07-25 13:14:22

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