SOLUTION: The numbers 1,2,3 can we written next to each other and with + and - signs you can get a sum of 0, ie 1+2-3=0. You can also do it for 1-4 by doing 1-2-3+4=0. It cannot be done for

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Question 987819: The numbers 1,2,3 can we written next to each other and with + and - signs you can get a sum of 0, ie 1+2-3=0. You can also do it for 1-4 by doing 1-2-3+4=0. It cannot be done for numbers 1-5.
i. Will it work for 1-6? 1-7? 1-8?
ii. In general, for which numbers will jt work?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
I set up my computer to find all the
possible results of 0 for the first n positive integers
up through n=8 with all possibilities of + and -
signs between them.  

There are no ways for 5 or 6,

There are 3,4,7,8 (lots of ways for 7 and 8. 

1+2-3 = 0

1-2-3+4 = 0

1+2-3+4-5-6+7 = 0
1+2-3-4+5+6-7 = 0
1-2+3+4-5+6-7 = 0
1-2-3-4-5+6+7 = 0

1+2+3+4-5-6-7+8 = 0
1+2+3-4+5-6+7-8 = 0
1+2-3+4+5+6-7-8 = 0
1+2-3-4-5-6+7+8 = 0
1-2+3-4-5+6-7+8 = 0
1-2-3+4+5-6-7+8 = 0
1-2-3+4-5+6+7-8 = 0

In fact the number of ways the number of solutions for 
1+-2+-3+-...+-n forms this sequence: 

0, 0, 1, 1, 0, 0, 4, 7, 0, 0, 35, 62, 0, 0, 361, 657, 0, 0, 4110, 7636, 0, 0,
49910, 93846, 0, 0, 632602, 1199892, 0, 0, 8273610, 15796439, 0, 0, 110826888,
212681976, 0, 0, 1512776590, 2915017360, 0, 0, 20965992017, 40536016030, 0, 0,
294245741167

So, it looks as though there are none for n 
1,2,5,6,9,10,13,14,etc.

Seems to follow a pattern.

Edwin
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