20 Anna randomly picked five integers from the following list
$$
53,62,66,68,71,82,89
$$
and discover that the average value of the five integers she picked is still an integer. If two of the integers she picked were 62 and 89 , find the sum of the remaining three integers.
20. Answer: 219
If we take modulo 5 , the seven integers $53, \underline{\mathbf{2 2}}, 66,68,71,82, \underline{89}$ give $3, \underline{2}, 1,3,1$, 2,4 . Hence the remaining three integers can only be 66,71 and 82 .