### 4 integers that can be combined with + or - to make the numbers 1 through 40

There are four positive integers, *a*, *b*, *c*, *d*, which can be combined using plus or minus to get all the integers from 1 to 40 inclusive. These combinations of *a*, *b*, *c*, and *d* can involve any number of *a*, *b*, *c*, and *d*, but none of these four integers can be used more than once. That is, some possible combinations are:

However, these types of combinations are not allowed:

What are the four integers?

*Probably more than a decade after I first heard this puzzle, I heard it again as the Puzzler on Car Talk #1143 (which originally aired around 2011, I think).*
SOLUTION

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