Socks in the dark, step by step
A drawer holds 8 red socks, 6 blue and 5 green, and the light is off.
How many socks must you take to be sure of a matching pair?
The worst that can happen, then one more
- Here is what is in there: 8, 6, 5 of the 3 kinds, 19 altogether, and you cannot see which is which.
- Do not count the cases — count the unluckiest run instead. There are 3 kinds here, so the worst that can happen is drawing one of each and still holding no pair at all.
- That is 3 drawn and no match. The very next one cannot be a new kind, because there are no new kinds left — so it must match something already in your hand: 3 + 1 = 4.
- So 4, and notice the numbers in the drawer never came into it. Eight of one and eighty of it give the same answer, and a child who added them up was answering a question that was not asked.
How it works.
- 01
Here is what is in there: 8, 6, 5 of the 3 kinds, 19 altogether, and you cannot see which is which.
- 02
Do not count the cases — count the unluckiest run instead. There are 3 kinds here, so the worst that can happen is drawing one of each and still holding no pair at all.
- 03
That is 3 drawn and no match. The very next one cannot be a new kind, because there are no new kinds left — so it must match something already in your hand: 3 + 1 = 4.
- 04
So 4, and notice the numbers in the drawer never came into it. Eight of one and eighty of it give the same answer, and a child who added them up was answering a question that was not asked.