6d (edited) • General discussion
Random Legos
You are building something awesome with Lego and need two bricks that are the same color. Because you are so captivated by your creation, you reach to grab them from a pile that has three different colors of the size brick you need without looking at them.
How many bricks do you need to grab to ensure that you have two of the same color?
What if you need three of the same color?
Advanced:
Can you figure out a general formula that tells you how many you need to grab given the number of same color bricks you need?
What if we changed the number of colors in the pile? Let's say that there are four colors in the pile and you need two of the same color, how many would you need to grab to get two of the same color in that case?
Mega Advanced:
What is the probability in the first situation that you could grab two of the bricks from the pile without looking and get the the same color?
Good luck and I'll post the rest of the answers soon!
The first two answers are below
- -
- -
- -
- -
- -
- -
- -
- -
- -
- -
- -
- -
- -
Answer: You might be tempted to think that you could just try your like and just take two, but we want to be absolutely certain. Let's think about the worst case that could possibly happen - you grab three and they are all the same color. If you take one more you will be certain to have two matching bricks, so you need to grab four.
If you need three of the same color, you can think the same way. It's possible to grab six bricks and have two of each color if you are unlucky, but if you grab one more, that is seven, you will be sure to have three of the same color.
This is an application of something mathematicians call The Pigeon Hole Principle. It says that if you have N pigeon holes and N+1 pigeons, you can be certain that there is at least one hole that has more than one pigeon in it. Sounds kind of silly and obvious but it turns out it to be incredibly useful in math.
1
0 comments
Random Legos
