There are two types of people in this world: those that can only lie, and those that can only tell the truth.
You might recognize that as the opening clause of so many knights and knaves problems. These are classic logic puzzles that I love to use to torture my siblings while we go hiking every summer. Which brings me to my real point. There are two types of people in this world: those that love math riddles, and those that despise them.
Sadly, my siblings fall into the second camp, but I’m hoping that you fall into the first.
What makes math puzzles so enticing are their pleasant blend of elementary math and logic. There are ones that require some knowledge of math, like maybe some knowledge of geometry or a clever use of arithmetic. And there are others that just require some logic. I always love watching mathematicians solve both types.
I recently had a visitor ask me the Cake Icing Problem. You have an iced birthday cake, you cut a piece of size Θ (that’s the center angle of the piece, the way you would typically cut a cake), flip it upside-down and place it back in the cake. If you continue on in one direction, cutting and flipping pieces of size Θ, will all the icing ever be back on top? Will it ever all be on the bottom? For certain values of Θ the answer is obvious, but can you say something general? Project Euler also poses a slightly trickier modification on the birthday cake puzzle.
A great treasure trove of puzzles is Varsity Math, a series cohosted by the Wall Street Journal Blogs and the National Museum of Math. A new couple of problems show up each week with solutions the following week. Last week there was a particularly fun one about areas of squares inscribed in squares.
Slightly less obvious in their mathematical nature, but no less fun, Popular Mechanics also hosts a Riddle of the Week. This week’s problem was the problem of 7 lit candles arranged in a circle. If you blow on one candle it changes the status of the two neighboring candles (that is lit with become unlit and unlit will become lit). What is the minimum number of moves to extinguish every candle. The solution is quite simple, and doesn’t really require any advanced knowledge of math but it’s a nice one to think about.
Alex Bellos, who posts his Monday Puzzle every two weeks, also wrote about a recent popular internet meme, the math problem for a 5 year old that’s been stumping the web. Bellos writes that these problems are sometimes interesting, but often totally misstated and impossible to solve. He walks us through one particular viral problem from earlier this month.
As you go forth and enjoy these puzzles, one word of advice: If you’re hiking up a mountain with a mixed group and you feel compelled to ask that cake icing problem, I recommend that you stay far back from the edge.