# Socks Probability interview puzzle

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?

**Answer** – 47 socks

**Explanation-**

10 socks of different colors ,and then we’ll pick remaining red (so we have 11) and then we pick three yellow(so we have 14) and we still have one pair of red and two pairs of yellow socks.

Then one of each of the remaining that would be 8. (So we have one pair of red, 2 pairs of yellow, 1 pair of each of the others) and another 8 of remaining twice (we 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

That is total 47 socks

15, as worse case scenario he picked one sock of each color – gives us 10 + 4 of the same color (again worse case scenario) + 1.

Question is asking for all pair of same colour, that is eaither all GREY or ORANGE or …….. etc.

Not like, 1Pair red, 1 pair yellow, 1 pair orange —— ALL PAIR of same colour required

Not at all, that makes not sense, they mean that each pair has 2 same color socks

47 as there is still a case when we take 46 socks and 3 pairs are not there

### Your Answer

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