Mathathon Sample Question 3

* Pretend you are color blind! *

Didn't came up with a clear explanation for "Cut each tablet in half, and take 4 halves." But I've used excel to visualize the outcome for other options. $\\$ First, you will not get sick for sure as scenario of taking the right combination of pills are here. $\\$ For "Take 1 tablet and cut the rest into halves, then take 2 halves." $\\$ $\\$ For this option, I've only listed the possibility of taking one of the A pills as the table will be similar for other pill. $\\$ For "Take 2 random tablets." $\\$ $\\$ (Typo in the picture. the probability should be 0.33) Forgive me for using a dumb way to solve it.

This is a well known logic puzzle.

We know that each day, you must eat one $A$ pill and one $B$ pill. With two days of supply, you therefore have two $A$ pills and two $B$ pills.

When you drop them on the floor, you don't know which order they are in, but that doesn't matter! The key thing to realize is that if you take whole pills, there's a chance you could be taking more than one pill for one of the types and none for the other type. Because of that, we can't take a whole pill.

However, if we use the fact that none of the pills are a mix of $A$ and $B$ , taking half of each pill will gives us in some order: $\frac{1}{2}A+\frac{1}{2}A+\frac{1}{2}B+\frac{1}{2}B=A+B$ . Thus, we got our desired amount! It helps to visualize things, so here is a picture.

One more thing. It's very easy to keep track of which pill was broken in half and which isn't yet broken. You can feel it in your hands. Thus, there's no chance of overconsumption.

Not A MATHEMATICAL solution.

Options 2 and 3 is out of consideration.

I thought about the problem and chose Cut each tablet in half, and take 4 halves as my answer. I got it right.

Everybody, here's a super easy Bonus - How do you know which tablets are cut and which ones aren't? Comment your answers below.