Sock Puzzle

[pdurrant]

After the extremely hard prisoners puzzle, here's an easy classic:

I keep my socks in a drawer. Every morning I get a clean pair out of the drawer. But I'm lazy — I never bother to pair up my socks after they're washed, I just bung them in the drawer as singles, and pick out a pair each morning. I don't really mind what colour socks I wear each day (so long as they're a pair), although I do like a little bit of variety, so I have more than one colour of sock.

This morning the drawer stuck — I could just open it enough to reach in to grab a sock, but I couldn't see what colour sock I was bringing out.

In the drawer (as I later worked out) were 10 black socks, 8 blue socks, and 5 brown socks (one got eaten by the laundry).

My bad luck didn't end with the stuck drawer. It took me the maximum number of goes it could have done to end up with a pair of socks

How many socks did I have to take out to end up with one pair, given that I was unlucky in the socks I pulled out?

Answers in spoiler tags please, even for this old chestnut.

[HarryT]

Spoiler:

It seems to me that the number of socks of each colour is a red herring; all that matters is the number of different colours.

You have three different colours. In the worst possible scenario, your first three selections will get you 1 black, 1 blue, and 1 brown sock. A fourth selection is guaranteed to get you a pair.

[pdurrant]

Originally Posted by HarryT

Spoiler:

It seems to me that the number of socks of each colour is a red herring; all that matters is the number of different colours.

You have three different colours. In the worst possible scenario, your first three selections will get you 1 black, 1 blue, and 1 brown sock. A fourth selection is guaranteed to get you a pair.

Exactly right. Where were you for the prison puzzle?

[Delta Tango]

If I understood correctly

Spoiler:

Most unlucky decision on the color would be brown, so asuming you decided on brown socks and are extremely unlucky, you'd take out all black and brown socks before getting the second brown one, so 10 + 8 (black + blue) + 2 brown ones = 20

edit:

Spoiler:

After reading the above spoiler:
It seems I misunderstood you. I thought you wanted some specific colour.

[poohbear_nc]

Originally Posted by pdurrant

Exactly right. Where were you for the prison puzzle?

He's probably still inside trying to work out how to escape!!!

[poohbear_nc]

Well - I think I can get this one.

Spoiler:

If you draw them out 1 by 1, after drawing out 3, the fourth sock has to match one of the original 3. So the fewest tries would be 2 (if you're lucky), the most tries would be 4 (if you're me).

[HarryT]

Spot on!

[poohbear_nc]

Originally Posted by HarryT

Spot on!

The first one I've been able to solve!!

[pdurrant]

Originally Posted by Delta Tango

If I understood correctly

Spoiler:

Most unlucky decision on the color would be brown, so asuming you decided on brown socks and are extremely unlucky, you'd take out all black and brown socks before getting the second brown one, so 10 + 8 (black + blue) + 2 brown ones = 20

edit:

Spoiler:

After reading the above spoiler:
It seems I misunderstood you. I thought you wanted some specific colour.

I can see how you might have misunderstood, I'll add some wording to clarify.

[obs20]

Here's my try:

Spoiler:

Seems that since there are only 3 colors and even while being unlucky, you'd still have a pair by the 4th sock.

[omk3]

Spoiler:

3 colours, so even if the first 3 socks you pull are different, the fourth has to match one of them. So 4 tries.

Wow, that was refreshingly easy

[pdurrant]

Originally Posted by obs20

Here's my try:

Spoiler:

Seems that since there are only 3 colors and even while being unlucky, you'd still have a pair by the 4th sock.

Spot on.

[pdurrant]

Originally Posted by omk3

Spoiler:

3 colours, so even if the first 3 socks you pull are different, the fourth has to match one of them. So 4 tries.

Wow, that was refreshingly easy

I thought everyone deserved a simple puzzle after the tar-pit of the last one. We even got HarryT to give an answer!

(& yes, you've got the right answer too.)

[Javed]

That one was easy!

Spoiler:

4 socks

[dreams]

I no longer wish you in that wonderful little prison you constructed, pdurrant.

I better have this one right, as everyone seems to think it was so easy...

Spoiler:

I stuck my hand in and grabbed a Black sock.

(So, as I'm usually late, and it always takes the longest possible time for me when I'm late..)

2nd time- Blue or Brown

3rd time - Blue or Brown (which ever I didn't get the 2nd time)

4th time- Eureka! It doesn't matter which color I get, it has to match one of the other 3 I already have , but only "given that I was unlucky in the socks I pulled out" previously.

answer: 4