There’s a Numberphile video that’s hurting people’s brains. It claims to prove (several ways, including in a companion video) that \[\sum_{n=1}^{\infty} n = -\frac{1}{12}\] This is, of course, highly counterintuitive. The video itself is misleading in that the speakers refer to the sum of all natural numbers, when this is not in fact the sum…
Category: Puzzles and Memes
Let’s Make a Deal
The Problem In the misnomered “Monty Hall” problem, the rules are set out as follows: You as the contestant are faced with the choice of three doors, behind exactly one of which is money or something else of significant value. You choose a door. The host, who knows where the money is, then opens a…
The Reversible Phone Number
Consider this problem: An absent-minded American mathematician has difficulty remembering his seven-digit phone number until he notices that, when he reverses the digits, he gets another seven-digit phone number that is a factor of his own phone number. After this point, he never has trouble with his number again. What is his phone number? (This…
The Baby Shower game: A Square Deal
The Puzzle Here’s an interesting puzzle: The hostess of a baby shower devises a game in which sixteen tokens are placed in an opaque bag. The tokens are all either pink or blue, and they’re otherwise identical in shape, weight, texture, and so on. Two guests are chosen. The first guest chooses a single token…
Three three-digit numbers
Here’s a fun little problem: Find three three-digit numbers that use each non-zero numeral once and add up to 999. Follow-up: How many such sets of numbers exist? If you want, take a moment to work on the problem on your own. Then continue reading. Finding a solution For the first question, any set of…
The Difference of Squares
In our Mathematical Reasoning class tonight, we discussed this problem: Can your age in years be written in terms of the difference of two square numbers? If so, what two numbers? There are at least three mathematical problems contained here: Given a specific whole number (0 or a positive integer), attempt to find two square…
Minimal Eulero
Eulero is a grid-based logic puzzle. Like Sudoku, it involves Latin squares; however, while Sudoku relies on a single Latin square, Eulero consists of two overlaid squares, one of numerals and one of letters. An additional constraint is that each letter-number combination has to appear exactly once. This got me thinking: What are the fewest…
Trick question memes
From time to time, a mathematical question of some sort will make its rounds on Facebook and other social media platforms. For instance, the one making the rounds most recently in my portion of the blogosphere was: \[5 + 5 + 5 – 5 + 5 + 5 – 5 + 5 \cdot 0 =…