Time for mango
- What are you doing?
- What does it look like I am doing?
- You are wondering if you can afford another glass of mango.
- Not exactly. Look at these five coins. What do you notice?
- That they are of two sizes. Two big ones and three small ones.
- Good. Now look at this.
- You are placing them so they all touch two other coins and an imaginary coin in the center.
- You are observant! Did I tell you that?
- My grandfather was a butler.
- Now look again.
- You do the same as before, but this time the two big coins don’t touch each other.
- Here is the challenge.
- I am already sitting down.
- Is the imaginary circle bigger now?
- Mango may do you good.
Problem source: Problem of the week, Math Forum.
June 25th, 2011 at 5:55 pm
So in the first arrangement the two big coins do touch each other.
I haven’t done the geometry but I think the circle in the centre will be smaller in the second arrangement, because there are 4 places where a small coin can “kern” next to a big one, enabling the coins to make a smaller ring, whereas in the first arrangement there are only 2 such places.