# Puzzles

## Venn Diagram Puzzles: Logic and Ambiguity

Puzzles involving two or three properties of people or objects, commonly solved by Venn diagrams, are popular with teachers, and perhaps not so popular with students! Several have asked about them recently, leading me to catalog our past answers about them, to find the most useful examples to point to. Some of these are very …

## A Challenging Divisibility Puzzle: Spoilers

(A new question of the week) Sometimes we give only minimal help on a question, to let a student puzzle over the problem and learn to figure it out herself. That may be enough, or we may go back and forth for some time, guiding her thinking until she finds the answer. In the latter …

## A Fermi Problem

(An archive problem of the week) A couple weeks ago, in discussing the value of estimates, I included one example of a (very simple) Fermi problem: one in which it is necessary to invent the data as well as the method of solution. Today, I will examine one answer in which we dug deeper into …

## Measuring Water with Two Containers

(A new question of the week) A recent question about an old puzzle leads to multiple references to our archive.

## Subtleties in a Logic Puzzle

(Archive Question of the Week) Logic puzzles can exercise our ability to reason carefully. Interestingly, the use of formal logic in doing so can actually get in our way, because such puzzles often have subtleties in their wording that are hard to capture in formal logic. Examining our thinking carefully can help us see wrong …

## Mathematical Thinking Solves an Operation Puzzle (Or Not)

(Archive problem of the week) Having just written about sequence puzzles, which sometimes can be solved mathematically, and sometimes are just psychological tests, I want to show a different kind of puzzle that I ran across while searching for those. At first, it looks like mere guess-and-check; then we find it can be solved easily …

## Pattern and Sequence Puzzles

One of the harder types of question to answer effectively is a puzzle, which as I define it means that there is no routine way to solve it, so any hint would likely give away the answer. But sometimes these are only “puzzles” to us, because we don’t know the context that would have told …

## When Math Doesn’t Make Sense

(Archive Question of the Week) One of my favorite questions, from 2001, asked about how to convince a skeptical friend, when a clear mathematical result goes against their intuition. Why should they believe the math? It led me into thoughts about the relationship of intuition to math, whether (and when) math can be trusted, and …

## Tracking Down the Meaning of a Problem

(Archive question of the week) Sometimes, we get a question that seems familiar, and can look back at past questions to see if we have already answered it, or to get ideas about what it means. This is the story of a problem that seems to float around as folklore, in varied forms. At first …