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 One is a sum (Posted on 2013-07-05)
a. How many 4 digit numbers are there such that at least one digit is a sum of 2 or 3 of the others?
b. How many 5 digit numbers are there such that at least one digit is a sum of 2,3 or 4 of the others?

The following conditions apply both for a and for b:
*The numbers consist of distinct digits.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer solution Comment 1 of 1

DEFDBL A-Z
FOR n = 1000 TO 9999
ns\$ = LTRIM\$(STR\$(n))
good = 1
FOR i = 1 TO LEN(ns\$) - 1
IF INSTR(i + 1, ns\$, MID\$(ns\$, i, 1)) THEN good = 0: EXIT FOR
NEXT
IF good THEN
good = 0
FOR one = 0 TO 1
t1 = one * VAL(MID\$(ns\$, 1, 1))
FOR two = 0 TO 1
t2 = t1 + two * VAL(MID\$(ns\$, 2, 1))
FOR three = 0 TO 1
t3 = t2 + three * VAL(MID\$(ns\$, 3, 1))
FOR four = 0 TO 1
t4 = t3 + four * VAL(MID\$(ns\$, 4, 1))
t = one + two + three + four

IF t > 1 THEN
IF VAL(MID\$(ns\$, 1, 1)) = t4 AND one = 0 THEN good = 1
IF VAL(MID\$(ns\$, 2, 1)) = t4 AND two = 0 THEN good = 1
IF VAL(MID\$(ns\$, 3, 1)) = t4 AND three = 0 THEN good = 1
IF VAL(MID\$(ns\$, 4, 1)) = t4 AND four = 0 THEN good = 1
END IF

NEXT
NEXT
NEXT
NEXT
IF good THEN
ct = ct + 1
END IF
END IF
NEXT
PRINT : PRINT ct

ct = 0

FOR n = 10000 TO 99999
ns\$ = LTRIM\$(STR\$(n))
good = 1
FOR i = 1 TO LEN(ns\$) - 1
IF INSTR(i + 1, ns\$, MID\$(ns\$, i, 1)) THEN good = 0: EXIT FOR
NEXT
IF good THEN
good = 0
FOR one = 0 TO 1
t1 = one * VAL(MID\$(ns\$, 1, 1))
FOR two = 0 TO 1
t2 = t1 + two * VAL(MID\$(ns\$, 2, 1))
FOR three = 0 TO 1
t3 = t2 + three * VAL(MID\$(ns\$, 3, 1))
FOR four = 0 TO 1
t4 = t3 + four * VAL(MID\$(ns\$, 4, 1))
FOR five = 0 TO 1
t5 = t4 + five * VAL(MID\$(ns\$, 5, 1))
t = one + two + three + four + five

IF t > 1 THEN
IF VAL(MID\$(ns\$, 1, 1)) = t4 AND one = 0 THEN good = 1
IF VAL(MID\$(ns\$, 2, 1)) = t4 AND two = 0 THEN good = 1
IF VAL(MID\$(ns\$, 3, 1)) = t4 AND three = 0 THEN good = 1
IF VAL(MID\$(ns\$, 4, 1)) = t4 AND four = 0 THEN good = 1
IF VAL(MID\$(ns\$, 5, 1)) = t5 AND five = 0 THEN good = 1
END IF

NEXT
NEXT
NEXT
NEXT
NEXT
IF good THEN
ct = ct + 1
END IF
END IF
NEXT n
PRINT : PRINT ct

2400

and

17496

 Posted by Charlie on 2013-07-07 12:25:57

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