Day: August 12, 2019

Perplexing Protons

You will need to use chemistry principles to solve this challenge.

You have some protons in a particle collider, but you don’t know how many. Your computers said there were 5 million at 12 noon based on their magnetic field. The problem is that you just found out that some electrons were leaking into the collider. You discovered the leak and patched it at 2pm. You know the electrons were leaking since 11 o’clock, and that they leaked at a constant rate. There are now 1 million electrons at 2:15, and they disrupted the magnetic field from which you counted the protons. However, some electrons collided with protons to make neutrons. You need to know how many protons there are for your experiment at 2:30. You don’t have time to count all the neutrons or recount the protons. You must figure it out based on the amount of energy released, which was 1 kilojoule. The challenge is to use the information above to determine the number of protons that will be in the collider at 2:30 if the rate of protons colliding with electrons is linearly proportional to the number of electrons.

solution

Complex Coins

You will need to use algebra and combinatorics to solve this challenge.

A normal coin has 2 flat sides and one thin round edge. When tossed, the coin always lands on a flat side. A brand new pencil has 2 small flat sides and 1 long round side. When tossed, the pencil always lands on the round side. Somewhere in the middle is the 3 sided coin, where all 3 sides are equally likely to be rolled. You happen to have 5 such 3 sided coins*. You call the 3 sides heads, tails, and round, or H, T, and R for short. You and your friend John a game with these coins. For every H, you get a point. For every T, John gets a point. But for every R, you both get a point. First to 5 points wins. You start playing, and roll 2 tails and a round. What is the probability that you win?

*Despite various lengthy efforts, nobody has been able to produce a perfect 3 sided coin as described in this challenge. So far. Some have come close, see “How thick is a three-sided coin?” from Standupmaths on Youtube, available below.

Solution