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

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.

# The Intervarsity Maths Competition

The Intervarsity Maths Competition is an annual one-day problem solving contest, typically held in March. Trinity usually sends two teams of four students to compete against other Irish universities for the top prize, though each student sits the test individually. It is an excellent opportunity to hone your problem solving skills and to meet members of other mathematical societies around Ireland. Selection test is usually held in February; all students are encouraged to take part.

Find some past tests here.

# Weekly Problem

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.

# Weekly Problems

# Previous Problems

### Freshers Week 2019

## Daily Problems

## Postgrad Orientation

## Saturday

## Monday

## Tuesday

## Wednesday

## Thursday

## Friday

### Problem Solving 2018/19

## Weekly Problems

### Refreshers Week 2018

## Daily Problems

## Monday

## Tuesday

## Wednesday

## Thursday

## Friday

### Freshers Week 2018

## Daily Problems

## Saturday

*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)?*

## Monday

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

## Tuesday

*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?*

## Wednesday

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

## Thursday

*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.*

## Friday

*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?*