# How many socks do you need to pick ?

+1 vote
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In your bedroom, you have a drawer with 2 red, 4 yellow, 6 purple, 8 brown, 10 white, 12 green, 14 black, 16 blue, 18 grey, and 20 orange socks. It is dark in your bedroom, so you cannot distinguish between the colors of the socks.How many socks do you need to take out of the drawer to be sure that you have at least three pairs of socks of the same color?

posted Apr 24, 2014

47
10 of different colors ,and then you pick remaining red (so you have 11) and then you pick three yellow(so you have 14) and you still have one pair of red and two pairs of yellow,
then one of each of the remaining that would be 8. (one pair of red, 2 pairs of yellow, 1 pair of each of the others) and another 8 of remaining twice (you will have 2 pairs of each of them) + another 8 of remaining +1

10(all diff) + 4(one red+3 yellow) + 8(one of each of remaining) -- one pair of each color
+ 8(all of diff colors) + 8 (all diff colors) -- 2 pairs of diff colors
+ 8 (all diff colors) + 1

= 47

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