A parent in one of my math classes passed this along to me. The National Museum of Mathematics (MoMath) has partnered with the Wall Street Journal to create Varsity Math. There are three levels: freshman, JV, and varsity. I was impressed with the JV problem, it wasn’t obvious and it really made you think. It is posted below.
Your friend tells you: This is a remarkable urn. It contains only red and black balls. If you reach in and take one ball at random, there’s an equal chance of drawing red or black. So you might think that if you instead take two at random, it’s 50/50 that your balls will match. Well, you’d be wrong—but if they do match, and then you reach your other hand in and take two more, your chances of matching a second time are 50/50!
How many balls in your friend’s urn (before you take any out)?
Comment below if you think you’ve figured it out. Beware, it is tricky. I had to read it about 5 times until I finally fully understood the situation.
Here’s a math discussion question to get your brain going 🙂 Can you think of a situation when 2+2 does not equal 4?
You’re first reaction is probably like mine…what?! That doesn’t even make sense! It always equals 4. That’s the whole point of math, isn’t it?
But step back and think about it for awhile. If we are counting objects than adding 2 objects to 2 other objects will always give you 4 objects. But what if we are not counting objects? There are other ways to think about numbers. What if instead we are talking about a clock? Imagine I tell you 11+2=1. That is true on a clock. 2 hours after 11 is 1. You do this in your head without thinking, you automatically know to count in a different way…a sort of circular way of counting.
In fact, you’ve been telling time for so long you can compute pretty quickly…especially if you have friends in Paris or India.
Or consider this scenario. Imagine you are at your home school co-op and the teacher is dividing the class into 3 groups by having people count off by 3’s. You’d like to be in the same group as your friends so you start counting in your head to see what group they will be in. Suppose you are in group 2 and one of your friends is 2 spaces away from you.
Because your friend will be in group 1. Another friend is 6 spaces away.
Hooray! That friend will be in your group. Suddenly you start noticing a pattern. If the spaces between you and your friend is a multiple of 3 they will be in the same group as you (so of course they start shuffling around trying to be in one of those spots).
The computations you made in your head are called modular mathematics. In this field of mathematics 2+2 does not always equal 4. You can read more about it here or go even deeper with this lesson.