Challenges

[SMcNeill]

What numbers between 1 and 1000 can NOT be expressed as the sum of consecutive integers?

ie 15 = 7 + 8 
  18 = 5 + 6 + 7

so neither one of these are in the set of numbers that can NOT be expressed as a sum of consecutive integers.

BONUS: one number can be expressed 15 different ways as a sum of consecutive numbers what is it and list the ways.

Here's my method that I've started testing with:  

Code: (Select All)

SCREEN _NEWIMAGE(800, 600, 32)

DIM ConInt(100) AS STRING



FOR i = 1 TO 100

    FOR j = 1 TO 100

        match = CheckMatch(j, i)

        IF match THEN ConInt(i) = ConInt(i) + STR$(j)

    NEXT

NEXT



FOR i = 1 TO 34

    PRINT i; ")"; ConInt(i)

NEXT

FOR i = 35 TO 67

    LOCATE i - 34, 30: PRINT i; ")"; ConInt(i)

NEXT

FOR i = 68 TO 100

    LOCATE i - 67, 60: PRINT i; ")"; ConInt(i)

NEXT



FUNCTION CheckMatch (start, limit)

    sum = start: inc = start

    DO

        inc = inc + 1

        sum = sum + inc

    LOOP UNTIL sum >= limit

    IF sum = limit THEN CheckMatch = -1

END FUNCTION

Short.  Simple.  Gives me the starting point to the numbers that you can consecutively add to, to make that number.

For example, at 15 it returns:  "1 4 7"
1 + 2 + 3 + 4 + 5 = 15
4 + 5 + 6 = 15
7 + 8 = 15

I'm not finding any numbers that can be found 15 different ways though.  The most I can come up with is 5 different matches to make the same consecutive number.

Or are you talking about a number that can be made from a string of 15 values?  I don't think that's possible either, as 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11  + 12 + 13 = 91.  Add more to it, and it becomes out of bounds ( > 100)

---

Oooohhhh....   Nevermind.  I can't read.  The limit was 1000, not 100.  LOL!!  My bad!

Still, the solution I have above holds up for us.  The limits just need to be increased, and you need a larger screen to print them all on, if you want to view them all at once!