The numbers $36,27,42,32,28,31,23,17$ are grouped in pairs so that the sum of each pair is the same. Which number is paired with 32 ?
The 8 numbers in the list have a sum of 236 .

When these 8 numbers are grouped into 4 pairs with equal sums, this sum must be $\frac{236}{4}=59$.

Therefore, 32 must be paired with $59-32=27$.

(Note that the pairings $36+23$ and $27+32$ and $42+17$ and $28+31$ satisfy the requirements.)

ANSWER: 27