Socks in the dark
The question
A drawer holds 8 red socks, 6 blue socks and 5 green socks, all mixed up. The light is off, so you cannot see what you are taking.
How many socks must you take to be sure of a matching pair?
The worst that can happen, then one more
865
#1#2#3
3+1=4
4· kinds:3· counts:did not matter
- There are 8, 6, 5 of the 3 kinds, and you cannot see which is which.
- Think about the unluckiest draws. With 3 kinds, you could draw one of each and still have no pair.
- The next one has no new kind left to be, so it must make a pair: 3 + 1 = 4.
- So 4. How many of each kind there are never mattered.
How it works.
- 01
There are 8, 6, 5 of the 3 kinds, and you cannot see which is which.
- 02
Think about the unluckiest draws. With 3 kinds, you could draw one of each and still have no pair.
- 03
The next one has no new kind left to be, so it must make a pair: 3 + 1 = 4.
- 04
So 4. How many of each kind there are never mattered.