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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 part 2 | Comment 2 of 3 |

DECLARE FUNCTION dr# (x#)
DECLARE FUNCTION sod# (x#)
DEFDBL A-Z
FOR d = 1 TO 9
IF used(d) = 0 THEN
used(d) = 1
FOR s = 1 TO 9
IF used(s) = 0 THEN
used(s) = 1
FOR t = 1 TO 9
IF used(t) = 0 THEN
used(t) = 1
FOR i = 0 TO 9
IF used(i) = 0 THEN
used(i) = 1
FOR n = 0 TO 9
IF used(n) = 0 THEN
used(n) = 1
FOR a = 0 TO 9
IF used(a) = 0 THEN
used(a) = 1
FOR h = 0 TO 9
IF used(h) = 0 THEN
used(h) = 1

tt = t * 11
ttttt = t * 11111
dinah = d * 10000 + i * 1000 + n * 100 + a * 10 + h
shore = ttttt - tt - 1994 - 1916 - dinah

d\$ = LTRIM\$(STR\$(dinah))

s\$ = LTRIM\$(STR\$(shore))
IF LEN(s\$) = 5 THEN
IF MID\$(d\$, 5, 1) = MID\$(s\$, 2, 1) AND VAL(MID\$(s\$, 1, 1)) = s THEN
o = VAL(MID\$(s\$, 3, 1))
r = VAL(MID\$(s\$, 4, 1))
e = VAL(MID\$(s\$, 5, 1))
IF used(o) = 0 AND used(r) = 0 AND used(e) = 0 THEN
dear = d * 1000 + e * 100 + a * 10 + r
hearts = h * 100000 + e * 10000 + a * 1000 + r * 100 + t * 10 + s
rose = r * 1000 + o * 100 + s * 10 + e
IF 3 * sod(dear) = 2 * sod(hearts) AND dr(rose) = 4 THEN
PRINT dinah; shore, t
END IF
END IF
END IF
END IF

used(h) = 0
END IF
NEXT
used(a) = 0
END IF
NEXT
used(n) = 0
END IF
NEXT
used(i) = 0
END IF
NEXT
used(t) = 0
END IF
NEXT
used(s) = 0
END IF
NEXT
used(d) = 0
END IF
NEXT

FUNCTION dr (x)
v = x
DO
v = sod(v)
LOOP UNTIL v < 10
dr = v
END FUNCTION

FUNCTION sod (x)
xs\$ = LTRIM\$(STR\$(x))
t = 0
FOR i = 1 TO LEN(xs\$)
t = t + VAL(MID\$(xs\$, i, 1))
NEXT
sod = t
END FUNCTION

finds

`DINAH  SHORE                T16903  23587                4`

 Posted by Charlie on 2010-07-25 13:54:53

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