Auto: : Bogosnov I.I.

All integers from -33 to 100 inclusive were arranged in some order, and the sums of each pair of adjacent numbers were considered. It turned out that there were no zeros among them. Then, for each such sum, the number reciprocal to it was found. The obtained numbers were added. Could the result be an integer?

#
Let's consider an example of such an arrangement. Consider the sequence $100, -33, 99, -32, \ldots, 34, 33$. Then, if the first number of the pair is in an odd position, the sum is 67. If it is in an even position, the sum is 66. The reciprocals will be $\frac{1}{67}$ and $\frac{1}{66}$, respectively, with the first occurring -67 times, and the second -66 times. Therefore, the final sum is 2.

## Answer

it is possible.

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