17. In a drawer in a dark room, there are 160 red socks, 80 green socks, 60 blue socks, and 40 black socks. A young man picks one sock from the drawer each time, but he cannot see the color of the sock he picks. How many socks must he pick to ensure that he has at least 10 pairs of socks?
(A) 21 ; (B) 23; (C) 24; (D) 30;
(E) 50
$\left|\frac{17}{\mathrm{~B}}\right|$
17. In any selection, at most one sock of a certain color will not form a pair, which happens if and only if an odd number of socks of that color are taken. Therefore, taking 24 socks is sufficient: because at most 4 of them will not form pairs, and the rest will have at least 20 pairs. However, 23 socks are enough! Because 23 is not the sum of 4 odd numbers, at most 3 of the 23 socks will not form pairs. On the other hand, taking 22 socks is not enough: if the red, green, blue, and black socks are $5,5,5,7$ respectively, there will be 4 socks that cannot form pairs, leaving only 9 pairs of socks, so 23 is the minimum number.