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 5 conditions to get 2 results (Posted on 2010-10-21)
A number N fulfills the following conditions:
1, It consists of nine distinct digits.
2. The inclusive sum of digits between the digits 1 and 2 is 12.
3. The inclusive sum of digits between the digits 2 and 3 is 23.
4. The inclusive sum of digits between the digits 3 and 4 is 34.
5. The inclusive sum of digits between the digits 4 and 5 is 45.

What are the lowest and the highest values of N?

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 computer solution | Comment 2 of 3 |

472918365
563819274

are the only two results and are therefore the lowest and highest by default.

DECLARE SUB permute (a\$)
CLS
a\$ = "123456789": h\$ = a\$
DO
a = INSTR(a\$, "1")
b = INSTR(a\$, "2")
c = INSTR(a\$, "3")
d = INSTR(a\$, "4")
e = INSTR(a\$, "5")

tot2 = 0
tot3 = 0
tot4 = 0
tot5 = 0

FOR i = a TO b STEP SGN(b - a): tot2 = tot2 + VAL(MID\$(a\$, i, 1)): NEXT
IF tot2 = 12 THEN
FOR i = b TO c STEP SGN(c - b): tot3 = tot3 + VAL(MID\$(a\$, i, 1)): NEXT
IF tot3 = 23 THEN
FOR i = c TO d STEP SGN(d - c): tot4 = tot4 + VAL(MID\$(a\$, i, 1)): NEXT
IF tot4 = 34 THEN
FOR i = d TO e STEP SGN(e - d): tot5 = tot5 + VAL(MID\$(a\$, i, 1)): NEXT
IF tot5 = 45 THEN

PRINT a\$

END IF
END IF
END IF
END IF

permute a\$
LOOP UNTIL a\$ = h\$

 Posted by Charlie on 2010-10-21 23:40:50

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