THE’Guess of socks in the dark It is one of those riddles that, once the answer is known, makes us sigh … “But it was obvious!”. Yet there are many people who remain deceived by its simplicity. The situation is this: in a drawer There are 10 white socks And 10 black socks in scattered order. They are exactly identical socks to the touch, so if the light is off, we cannot distinguish them. We therefore assume that the light is just off and I want to be sure of fishing Two socks of the same color:
What is the minimum number of socks I have to fish?
Try to give an answer, which we now see the solution together.
The solution to the abdomen of socks in the dark
If you are still thinking, don’t worry, it’s normal. Often when a problem like this is presented, those who are not accustomed to mathematics or logic is “blocking” fromimpression that some dark calculation is hidden behind the solution insidious. In this specific case, you are led to think that it is some calculation of chance, That perhaps we knew in high school but that surely today we forgot.
But it is absolutely not so, the answer to the indovin is extremely simple And just reflect concretely on the problem to find the solution. Let’s go for steps, fishing a sock at a time:
- Peach the First sock: It can be both white and black. Suppose it is black (the reasoning is also worth if we decide to suppose that it is white).
- So I peek a Second Calzino And this could also be both black and black. We fish another black, we won: we already have our couple of black socks. But we could fish one white And then find ourselves with a black and white sock, and therefore we are not happy. You need a third sock.
- We arrive at the fishing of the third sock, He too can be both black and black. In case it was black, we won! Finally we are with Two black socks And One white. But if it was white instead? We would have won the same, because we would find ourselves with A black sock And Two whites.
In short, if we fish two socks we are not happy, because we could have two of different colors. But if we fish three, we will certainly have a pair of identical socks, because there are only three options:
- I fished three socks of the same color – whether they are all white or all black – and therefore I certainly have two of the same color in hand;
- I fished two black socks and one white, and therefore I have two socks of the same color, black;
- I caught two white socks and one black, and therefore I have two equal, white socks.
