If you have black socks and brown socks in your drawer mixed in a ratio of 4 to 5, how many socks will you have to take out to make sure that you have a pair the same color?
Minimum number of socks is three (3).
This is tricky question. The answer is 3 minimum pairs.
First thing, The question does not insist upon the number of trails that you may make in order to get the same coloured pairs. It simply asks for the minimum number of socks required.
The second thing, mixed in the ratio of 4 to 5 is redundant and is not required for getting to the answer.
Well, that's a tricky sock situation you've got there! To guarantee a matching pair, you must have at least three socks. Let me explain: if you pick out two socks and they happen to be the same color, congratulations! You've got a pair. On the other hand (or foot), if you pick out two socks of different colors, say black and brown, you'll need to pick just one more sock to ensure you have at least one pair of the same color. So, three socks is the answer! Just remember, the more socks you pick, the greater the chance of finding a matching pair—and the more fun sock puppet shows you can have!
To determine the minimum number of socks you need to take out to ensure you have a pair of the same color, you'll need to apply the Pigeonhole Principle.
In this case, we have black socks and brown socks in a ratio of 4 to 5. To guarantee a pair of the same color, we need to find the worst-case scenario. This means we assume that every time we pick a sock, it will be of a different color than the previous one.
Starting with the assumption that all the black socks are picked first, we calculate the maximum number of socks needed to exhaust the supply of black socks. Since there is a ratio of 4 black socks to 5 brown socks, and we want to find the maximum number of black socks, we can divide the total number of socks by the sum of the ratios (4 + 5 = 9). Let's assume we have 9x socks (where x is a positive integer). In this situation, we have 4x black socks and 5x brown socks.
Now, we calculate the maximum number of black socks that can be picked before encountering a brown sock:
Total number of socks - Maximum number of black socks = Maximum number of brown socks
(9x) - (4x) = 5x
Therefore, to ensure we have at least one pair of black socks, we need to pick a maximum of 5x + 1 sock.
In other words, you need to take out a minimum of (5x + 1) socks, where x is a positive integer.
assuming you have full pairs, then the minimum number of socks is 8+10 = 18.
So, you need to take out 9 socks to be sure there is at least one of each color.