## Holiday puzzles

We at Problem of the Week would like to wish you a wonderful, very restful holiday! For those of you…

## Prime Numbers in Nature: Cyclical Cicadas

To many, the prime numbers are a foreign and useless concept conjured up in the laboratories of decrepit mathematicians, having…

## Problem of the Week (41)

Chloé chooses a real number uniformly at random from the interval . Independently, Laurent chooses a real number uniformly at random…

## Problem of the Week (40)

Among the constants , there are equal to and equal to . Find the sum of all the products ,…

## Problem of the Week (39)

Compute the sum of all positive integers for which the expression is an integer. Source: HMMT February 2021 (Harvard-MIT Mathematics…

## Problem of the Week (38)

What is the least possible value of for all real numbers ? Source: AMC 12A 2021 Happy problem solving! Email…

## Problem of the Week (37)

Leo the fox has a 5 by 5 checkerboard grid with alternating red and black squares. He fills in the…

## Problem of the Week (36)

In the tribe of Zimmer, being able to hike long distances and knowing the roads through the forest are both…

## Problem of the Week (35)

This an incredible problem—incredible because it seems to lack sufficient data for a solution. A cylindrical hole six inches long…

## Problem of the Week (34)

The solution of the equation can be expressed in the form . Find . Source: AMC 12A 2010 Happy problem…

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