2 October 2013

# Puzzle: Assorted socks

Flying back from DC. Puzzle time. I am switching back to logical/math puzzles since the word puzzles were not much popular last time.
As always, send me personal messages on FB. Do not write your answer on the comment section to give others a chance to try the problem.

In a basket, there are 8 pairs (16) of black socks, 7 pairs (14) of white socks, 6 pairs of red socks, 5 pairs of blue socks, 4 pairs of green socks, 3 pairs of yellow socks, 2 pairs of purple socks and 1 pair of pink socks.
Assume that there is no difference between a right sock and a left sock.
If you are blindfolded, how many MINIMUM number of socks do you have to pick to guarantee 3 pairs (six) of socks that are of the same color (any color will do)?

Posted October 2, 2013 by Rajib Roy in category "Puzzles

1. By Rajib Roy (Post author) on

Answer: The best way to think about this problem is to think about the worst case – what is the maximum you can pick up without picking up six of any?
Well, you would pick both the pink socks, all four of the purple socks and then 5 yellow socks, 5 green socks, 5 blue socks, 5 red socks, 5 white socks and 5 black socks.
So far we have 36 socks and we have managed to avoid picking six of any. There are no more options left. The 37th sock – any which one you pick – will make a sixth of some color.
So the answer to the minimum number you have to pick to GUARANTEE six socks of one color is 37.

2. By Rajib Roy (Post author) on

My thought process would – first pick one of each color. Then the next one I pick would definitely be a pair. The worst case after that is if I keep picking the same color as the previous one till I run out. Thus the worst is Initial 8 plus the next 15 are black. Then I would proceed with all the 13 white socks…. so I guess 64? (8+15+13+11+9+7 and the next one will force a sixth pair)

3. By Rajib Roy (Post author) on

BTW, Devashish, my assumption was you want minimum number to GUARANTEE 6 matched pairs. And they are different color pairs.

4. By Rajib Roy (Post author) on

If you can live with the 6 pairs being not necessarily of all different colors, then my thought process would be that the worst case – first 8 of different colors. 9th is a match. Take the 10th as the same as the matched color – so now you have 8 unmatched color. 11th is a match. Pick 12th as the same color …. I think the 19th will force a sixth pair as long as you don’t want different colors necessarily.

5. By rajibroy (Post author) on

Jamie, it means -” I have none of those hang ups. Shorts. Half sleeve shirts. I do not even need a comb” 😉

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