There are several groups of six integers whose product is 1 . Which of the following cannot be the sum of such a group of six integers?
(A) -6
(B) -2
(C) 0
(D) 2
(E) 6
For the product of two integers to equal 1, the two integers must both equal 1 or must both equal -1 .

Similarly, if the product of six integers is equal to 1, then each of the six integers must equal 1 or -1 .

For the product of six integers, each of which is equal to 1 or -1 , to equal 1 , the number of -1 s must be even, because an odd number of -1 s would give a product that is negative.

That is, there must be zero, two, four or six -1 s among the six integers.

We summarize these four possibilities in the table below.

| Number  of -1 s | Product of the  six integers | Sum of the  six integers |
| :---: | :---: | :---: |
| 0 | $(1)(1)(1)(1)(1)(1)=1$ | $1+1+1+1+1+1=6$ |
| 2 | $(-1)(-1)(1)(1)(1)(1)=1$ | $(-1)+(-1)+1+1+1+1=2$ |
| 4 | $(-1)(-1)(-1)(-1)(1)(1)=1$ | $(-1)+(-1)+(-1)+(-1)+1+1=-2$ |
| 6 | $(-1)(-1)(-1)(-1)(-1)(-1)=1$ | $(-1)+(-1)+(-1)+(-1)+(-1)+(-1)=-6$ |

Of the answers given, the sum of such a group of six integers cannot equal 0.