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
47. The worst case is that we take first 10 socks of different colors than we take 1 red and 3 yellow and 8 of each different color. So now we have one pair of each color. We repeat it 3 more times so now we have two pairs of each color + 1 sock of a pair from each color. So now we take only one sock and we are sure we have 3 pairs of the same color. Total 10+4+4*8+1 = 47
Your Answer
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