Exercise your brain weekly

Welcome to the Mathsoc Problem Solving page run by our Quizmaster, Cillian.

Problem solving sessions are held every Monday at 6:00pm in the New Seminar Room.

Check out our Facebook group here.

Also check out our involvement in the Irish Mathematical Intervarsities and IMSA here.

This year’s Intervarsity Maths Competition will be hosted by Trinity, and will be on Saturday, the 30th of March. The selection test will take place on Monday, the 25th of February, from 6pm to 9pm, (maybe in the New Seminar Room, but it might not be big enough, this will be confirmed) instead of normal problem solving that night. I would encourage as many of you as possible sit the selection test and I hope to see you all there!

~ Cillian

The selection test will be set by Pete. Find some past tests here.

Think you have a solution? Email it to [email protected] or contact the Quizmaster here. Previous Weekly Problems can be found in the files below.

Problems 12

Problems 11

Problems 10

Problems 9

Problems 8

Problems 7

Problems 6

Problems 5

Problems 4

Problems 3

Problems 2

Problems 1

Intro Problems 1

A donut shop has 8 different types of donuts. How many different ways are there to choose 4 donuts from these 8 types (assuming there are at least 4 donuts of each type)?

How many ways are there to cover a 2xn board with n dominoes (each of size 2×1)?

Three students take a strange module where, instead of a final exam, the students are given a challenge. The professor has nine hats; three red, three green, and three blue. Each student is given a hat in a way that all students know the colour of every other student’s hat, but not their own. The students simultaneously guess the colour of their own hat by writing it down. If they are all incorrect, they all fail the class. If any student is correct they all pass. Before this challenge occurs, the rules are explained to the students and they are given time to come up with a strategy. It there a way for the students to guarantee they will pass? If so, how can it be done?

A fast food restaurant sells chicken nuggets in packs of 4 and 9. What is the largest number of nuggets that cannot be ordered?

32 dominoes can cover a chessboard. If two opposite corner squares are removed, is there a way to cover the remaining 62 squares with 31 dominoes? If so, show how it can be done. If not, explain why it is impossible.

Given a white 8×8 grid, how many different ways are there to paint 32 of the squares black such that every 2×2 square on the board contains exactly 2 black squares and 2 white squares?