## Maximizing the Product: A Problem

This week I offer a problem: What is the largest possible product you can make with a group of positive integers if the sum of those integers is 2017? Here we do not assume that the integers are distinct from… Continue Reading

My last post put forward the challenge to find numbers whose binary representations end with their decimal representations, like how $11 = 1011_2.$ It turns out that there are lots of them. Infinity of them, in fact. If we’re going to… Continue Reading

## Binary Patterns: A Puzzle

Imagine a world in which there are only 2 digits. We are used to having 10 digits, from 0 to 9, but with just 2 of them, we’d be limited to 0 and 1. We could count in that world… Continue Reading

## Infinity

Generally speaking, people are not indifferent to math. When I introduce myself as a mathematician, I rarely get the disinterested “oh”s I’d expect if I were instead middle management at an unfamiliar, generically-named firm. Sometimes I get math horror stories,… Continue Reading

## A Mathematician’s First Camping Trip

My son has reached the age where being a scout means being outdoorsy. Last weekend, he and I went on our first camping excursion with his den. Scouting urges to BE PREPARED, and I didn’t want to be the one… Continue Reading

## Cardan Grilles: A Solution

In my last post, I challenged the reader to fill out this letter grid… …so that no matter how the Cardan grille below is placed on top of it, the letters showing through the holes would spell out a word. Combining… Continue Reading

## Cardan Grilles: A Challenge

Throughout history, people have tried to find ways to pass hidden messages. The problem is that as soon as someone sees a conspicuous-looking note, they immediately try to figure out what the secret is; if you saw a piece of… Continue Reading

## Not Quite 11 Triangles

A few mornings ago, my son and I were sitting on the couch waking up to the day. I was sipping my coffee and he was just staring up at the ceiling. He broke the silence to ask me, “Dada,… Continue Reading

## Pythagorean Days

Those of you who have been obsessing about today’s solar eclipse may have missed another equally amazing event just last Tuesday: the date, 8/15/17, made a Pythagorean triple. A Pythagorean triple is a group of three positive integers that satisfy… Continue Reading

## A Mathematician Wears a Bracelet

For my birthday this year, my son fashioned me a bracelet out of a pipe cleaner and some glittery green beads. There was just one problem, though: He didn’t account for his dad’s big hands. Lucky for me, I’m a… Continue Reading