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?

since sum of 4 to 5 is 45 then 4 and 5 are the end points, assume 4 is first so we have 4-------5
now for the 3 to 4 sum we can not use 5 obviously so the numbers strictly between 3 and 4 sum to 34-3-4=27 and the numbers to the right of 3 and before 5 sum to 45-34-5=6
now the numbers left to sum to 6 are 1,2,6,7,8,9 so the only way to get 6 is with 6 itself, that means we have
4-----365
now the 2 to 3 sum is 23 and by similar reasoning we get
472---365
and similar reason with 1 to 2 gives us
472-18365
and only one place left for 9
472918365
and by starting with 4 on the other side we get the reverse of
563819274
and since they are the only 2 solutions these are the max and min

Posted by Daniel on 2010-10-22 02:35:35