5. Seven fishermen stand in a circle. The fishermen have a professional habit of exaggerating numbers. Each fisherman has a measure of lying (each has their own, an integer) - how many times the number mentioned by the fisherman is greater than the true value. For example, if a fisherman with a lying measure of 3 catches two fish, he will say he caught six fish. In response to the question: "How many fish did your left neighbor catch?", the answers (not necessarily in the order in which the fishermen stand) were $12,12,20,24,32,42$ and 56. In response to the question: "How many fish did your right neighbor catch?", six fishermen answered $12,14,18,32$, 48,70. What did the seventh fisherman answer?
Solution. Note that the product of all the numbers named by the fishermen in each of the surveys is the product of the number of fish caught, multiplied by the product of all the measures of lying of these fishermen. Therefore, the seventh answered $\frac{12 \cdot 12 \cdot 20 \cdot 24 \cdot 32 \cdot 42 \cdot 56}{12 \cdot 14 \cdot 18 \cdot 32 \cdot -48 \cdot 70}=16$.

Note that such a situation could indeed arise if the fishermen caught $2,7,3,8,4,2,2$ fish, and their measure of lying was $10,6,6,8,7,8,6$, respectively.