Good and Bad Mathematical Problems

Two splendid problems, one terrible one and one intermediate one, all courtesy of brilliant.org.

INTRODUCTION

This week on brilliant.org I have encountered two of the finest mathematical problems that I have seen on that site, and also unequivocally the worst. In the rest of this post I will share these problems with you – solutions and explanations will appear in a later post.

FIRST THE BAD NEWS

This is the terrible problem referred to in the introduction. In almost 15 months og being a brilliant.org solver I have complained about precisely one problem – this one:

bad problem

The “correct” answer when I give it will make it clear precisely why I was so annoyed by the setting of this problem.

TWO FABULOUS PROBLEMS

These two problems were beautifully set, very fun to solve, and one has a published solution that I consider to be quite superb. First:~
Mendrin Circles

I tackled this one this very morning:

Mr Mediocre question II

A BONUS PROBLEM

Can you give Honey the ant maximum possible access to the surface of the cube?

Honey the ant