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**tony123****Member**- Registered: 2007-08-03
- Posts: 189

It is possible to replace each of the ± signs below by either – or + so that

± 1 ± 2 ± 3 ± 4 ± ... ± 96 = 1996.

At most how many of the ± signs can be replaced by a + sign?

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

1+2+3+4+5+...+76 - 77 + 78+...+82 - 83 - 84 - ... - 95 - 96 = 1996.

ie. there are + signs before the numbers from 1 to 82 inclusive, except for 77.

This means that the maximum number of + signs in the equation is 81.

Why did the vector cross the road?

It wanted to be normal.

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