Problem of the Week (17th Jan, 2022)
The positive integers are the smallest that satisfy the equations: If , where and are positive integers, then what is ? Source: Ritangle, Stage 1,…
Problem of the Week (10th January, 2022)
There are 8 lily pads in a pond numbered 1,2,…,8. A frog starts on lily pad 1. During the -th second,…
Problem of the Week (13th December, 2021)
You have a sphere, the points on the surface of which can be colored white or black. You are told…
Problem of the Week (6th December, 2021)
Given an infinite lattice of points, colored with 5 colors, prove that it is always possible to find a monochromatic…
Problem of the Week (29th November, 2021)
Let be the positive integer , a -digit number where each digit is a . Let be the leading digit…
Problem of the Week (22nd November, 2021)
There are 5 couples attending a party. Everyone shakes hands with the people they don’t know. John asks everyone at…
Problem of the Week (Nov 15, 2021)
Three boys, Arthur, James, and Zain, are working on a set of math problems, each of equal difficulty. Together, they…
Problem of the Week (Nov 8, 2021)
Paul starts at 1 and counts by threes: 1, 4, 7, 10, . . . . At the same time and at the same…
Holiday puzzles
We at Problem of the Week would like to wish you a wonderful, very restful holiday! For those of you…
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…