# how many socks?

phil3000
Posers and Puzzles 06 Feb '09 17:21
1. 07 Feb '09 10:41
Originally posted by FabianFnas
One box only, and 1 dozen identical pairs of shoes, all of them in the same box.
It's dark (as in a coal mine) and I pick up x number of shoes. What is x in order to be sure that I pick up a pair that I can use for my daily promenade?

No loophole and one box only. How many shoes do I need to pick up?
Ah my mistake, I meant 7 shoes when i said 7 boxes, however, if you have 12 pairs (my mistake again 😳) instead of 12 shoes, then n = 24 so you would then require 13 shoes to make a pair.

I hope.
2. 07 Feb '09 10:54
Ah my mistake, I meant 7 shoes when i said 7 boxes, however, if you have 12 pairs (my mistake again 😳) instead of 12 shoes, then n = 24 so you would then require 13 shoes to make a pair.

I hope.
Now you got it right.
13 shoes and at least one of the is a left shoe, and 1 of them is a right shoe.

The socks problem again: In the original problem there were two colours of socks, white and black.
In my box of socks there are three colours: black, white, and red.
How many have I to take up from the box in order to have two socks in the same colour?
3. 07 Feb '09 11:31
Originally posted by FabianFnas
Now you got it right.
13 shoes and at least one of the is a left shoe, and 1 of them is a right shoe.

The socks problem again: In the original problem there were two colours of socks, white and black.
In my box of socks there are three colours: black, white, and red.
How many have I to take up from the box in order to have two socks in the same colour?
Presumably 4, Worst case, you'll get 1 of each and the 4th one will match one of the first 3.
4. 07 Feb '09 12:38
Presumably 4, Worst case, you'll get 1 of each and the 4th one will match one of the first 3.
So in the socks problem, can you produce a formula f(n) = number of socks you have to pick in order to have a pair, depending of number n of colours of the socks?

Say that you have to pick socks for you *and* your wife/husband from a box with n number of colours, how many socks do you need to pick in order to satisfie both you and your wife/husband at the same time? How do you change the formula to include her/him?
5. 07 Feb '09 12:53
Originally posted by FabianFnas
So in the socks problem, can you produce a formula f(n) = number of socks you have to pick in order to have a pair, depending of number n of colours of the socks?

f(n) = n + 1

Say that you have to pick socks for you *and* your wife/husband from a box with n number of colours, how many socks do you need to pick in order to satisfie both you and your wife/husband at the same time? How do you change the formula to include her/him?

To find two pairs f(n) = n + 3
6. 07 Feb '09 12:55
So with n colours, to find p pairs we have:

f(n, p) = n + (p*2) - 1
7. 07 Feb '09 14:072 edits
sounds to me like 13 shoes are needed to guarantee a pair, since it is possible to unluckily choose all 12 of the "left" shoes and thus not make a matching pair until you pick one more. unlike the black/white sock scenario, in this one a "left and a left" (analogous to choosing a "black and a black" or a "white and a white" in the previous problem) does NOT constitute a pair. so you are required to choose enough shoes to guarantee at least one right to go with your 12 lefts (WLOG of course, since the reasoning can be switched around as "one left to go with your 12 rights." )

EDIT: i just realized that there was a second page of posts, and clearly this question was already answered. now onto your next question: Say that you have to pick socks for you *and* your wife/husband from a box with n number of colours, how many socks do you need to pick in order to satisfy both you and your wife/husband at the same time?

this is a trick question, since women are never satisfied. (an alternate, and equally funny, response is: "if i knew how to satisfy both myself and my wife at the same time, i'd be a happily married man." 🙂 )
8. 08 Feb '09 05:44
Same scanario as the socks but this time it's gloves.

You have 6 black fur lined gloves and 6 brown fur lined gloves in a drawer.
Dark room, no light etc.etc...

You can try them on in the dark to make sure you get a left and right pair.

So How many gloves do you take out to ensure you get a matching pair?

If you are unlucky enough to choose a black glove and a brown glove
then turn them both inside out. Ta Da.... a matching pair.
9. AThousandYoung
A Hispanic Invention
08 Feb '09 18:20
Originally posted by phil3000
In my drawer i have ten black socks and ten white socks , i am going out to a party so i need a fresh pair of socks ,as i open the drawer the bulb blows and i can,t see a thing , because i am in a rush to get to the party i stick my hand in and scoop up some socks . what is the minimum amount of socks i can get out to have a matching pair?
I think if I sock you six times you'll give me the answer.
10. AThousandYoung
A Hispanic Invention
08 Feb '09 18:21
Originally posted by greenpawn34
Same scanario as the socks but this time it's gloves.

You have 6 black fur lined gloves and 6 brown fur lined gloves in a drawer.
Dark room, no light etc.etc...

You can try them on in the dark to make sure you get a left and right pair.

So How many gloves do you take out to ensure you get a matching pair?

If you are unlucky e ...[text shortened]... ose a black glove and a brown glove
then turn them both inside out. Ta Da.... a matching pair.
But then one will have black fur and the other brown fur. No good!

And they'll be scratchy 🙁.
11. 09 Feb '09 01:26
Same scenario as the socks and the gloves - but this
time you have two complete chess genuine Staunton chess
sets laying loose in the drawer.

How many pawns and pieces do you have to take out
to ensure you can have one full set and enough for a game.
12. 09 Feb '09 07:29
Originally posted by greenpawn34
Same scenario as the socks and the gloves - but this
time you have two complete chess genuine Staunton chess
sets laying loose in the drawer.

How many pawns and pieces do you have to take out
to ensure you can have one full set and enough for a game.
if you can't tell the difference between pawns/pieces by touch, i think you need to take out 63 pieces in case the last two are both the same single piece (make sure they're not both black/white queen/king) because that would require you to pick pieces down to the last two
13. 10 Feb '09 00:56