Puzzles for All – MATHS WEEK IRELAND (2024)

Puzzles for Alladmin2023-11-30T14:31:11+00:00

Puzzles are a fun and enjoyable way to challenge yourself and improve numeracy. They allow you to develop problem solving skills without even trying!

Here you will find a selection of puzzles, problems and brainteasers for all ages. Try them out yourself and with those around you.

Matchstick Puzzles

Click on the image to try some matchstick puzzles.

12 Days of Christmas puzzles

Click the class groups below for a puzzle PDF:

Older primary

Younger primary

How many siblings?

Mary has twice as many brothers as sisters, while her brother John has twice as many sisters as brothers. How many children are there in their family?

Solution

Answer: 4 children altogether

Mary has 2 brothers and one sister, while John has 2 sisters and 1 brother.

This sort of puzzle can be solved using a technique called simultaneous equations. This is a technique that is covered in Junior Certificate mathematics and is very powerful in finding unknown quantities in a system if one has enough information to piece together mathematically. It’s not really necessary for the above question that may be solved by in- formed “trial and error”, but we will take the opportunity of showing the technique here.

We have two related pieces of information:

1. Mary has twice as many brothers and sisters

2. John has twice as many brothers as sisters

We can express each of these with symbols and numbers. We use symbols as a shorthand code.

Here we will use the letter B to represent the number of boys and the letter G to represent the number of girls

1. “Mary has twice as many brothers and sisters” can be expressed symbolically.

How many texts?

Pete, Sarah, Matt, Amy and Luke are all friends. Each of them sends one text message to each other person. How many messages are sent in total?

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Solution

Answer: 20

This problem again relates to graph theory but this time the relations between each of the objects is different:

Pete will sendfourtext messages: one to Sarah, one to Matt, one to Nina and one to Arturas.

Sarah, who has already received a text message from Pete, still needs to sendfourmessages – one to each person.

This is the same for Matt, Nina and Arturas meaning that a total of20text messages will be sent.

Handshake puzzle

Amy, Liam, Samira and Luke meet up. Each person shakes hands with every other person once.How many handshakes are there in total?

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Solution

Answer: 6

Displaying this puzzle in a square format allows for a visual solution and also an introduction to graph theory. This is the study of graphs where a graph is used to demonstrate relations between objects. In this case we are demonstrating the relations between four people.

We can see that Amy (in the red jumper) will have a total of3handshakes: one with Liam, one with Samira and one with Luke.

Liam has already shaken hands with Amy so he will havetwomore handshakes: one with Samira and one with Luke.

Samira will have already shaken hands with Amy and Liam so she will only haveonemore handshake with Luke.

Luke, at this stage, will have shaken hands with everyone in the group.

There will be a total ofsixhandshakes for four people.

World Cup puzzle

There are 6 teams in a group. Each team plays every other team twice. How many games are there in total?

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Solution

Answer: 30 games

This problem is more like the handshake problem and again introduces pupils to graph theory.

Let’s take Group D with the six teams of Republic of Ireland, Wales, Austria, Serbia, Moldova and Georgia.

Republic of Ireland will playtengames: two against Wales, two against Austria, two against Serbia, two against Moldova and two against Georgia.

Wales will have already played the Republic of Ireland twice so they will haveeightgames left to play: two against Austria, two against Serbia, two against Moldova and two against Georgia.

Austria will have already played the Republic of Ireland and Wales so they will havesixgames left to play against Serbia, Moldova and Georgia.

Serbia will have played against the Republic of Ireland, Wales and Austria so they will havefourgames left to play against Moldova and Georgia.

Moldova will have played every team twice at this stage apart from Georgia.

Georgia will then have played every team in the group twice.

There will be a total of 30 games for a group of six teams.

Expanding car park

A client wants to double the size of his car park (shown left).He insists on retaining a square shape and as many of the trees as possible. What is the best solution?

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Solution

Honeycomb puzzle

Arrange the numbers 1-19 in the honeycomb grid (left) so that each row, column and diagonal adds to 38. You can only use each number once and every number must be used.

Teacher’s/parent’s note: the difficulty of this puzzle can be altered by providing some of the numbers as a starting point. Logic and reasoning will then allow pupils to complete the puzzle!

Download and print honeycomb grid

Solution

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Space mission

A rocket blasts off from Earth heading for Mars, getting faster as it travels. In fact, the rocket’s speed doubles every week that it’s in space. If the rocket lands on Mars in week 12, in which week was it halfway there?

Solution

Answer: week 11

Attacking the castle

A square medieval castle sits on a square island surrounded by a square moat and was under siege. All around the island, there is a 5 metre wide water moat. There’s ground on the other side to rest the bridge on (if you can get it to stretch that far).

The attacking king sent his men back to build two wooden foot bridges. Unfortunately these clever men came back with two bridges exactly 5 metres long. (that meant that they couldnt be supported on the ground at both sides of the moat). They have no nails or rope is there any way they can get across?

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Solution

Calculations

	By Pythagoras the distance across at the corners can be calculated: 5²+ 5²= 50 ?50m = 7.07m
	Assuming a support overlap of 0.15m will be steady enough it is possible

Moving coin puzzle

These moving coin puzzles were popularised by the great English puzzler Henry Dudeney. They can be played with coins, buttons, counters or any objects that make two distinct sets.The aim of this “E” puzzle (so-called because of its shape) is to reverse the positions of the Green and Red counters in the grid.There are rules of course to make it challenging:

There is no passing or jumping.
Only one piece at a time can be in the same square.

Download and print A4 grid

How old is Lucy?

Sarah is three times as old as Peter. Max is twice as old as Peter. Lucy is two years older than Max. Altogether their ages sum to 26 years. How old is Lucy?

Solution

One way to solve this puzzle is by using equations. From the information given, we can write the following equations (initial’s are used to denote the child’s age):

S = 3P (Sarah is 3 times as old as Max)
M = 2P (Max is 2 times as old as Peter)
L = M + 2 (Lucy’s age is equal to Max’s age plus 2 years)
S + P + M + L = 26 (the sum of all 4 children’s ages is equal to 26)

Then we can substitute into Equation 4:

3P + P + 2P + 2P + 2 = 26

By standard algebraic rules,

8P +2 = 26

8P = 26 – 2 = 24

P = 24/8 = 3

We now know that Peter is 3 years old, and Max is twice Peter’s age (Equation 2), therefore Max is 6.

Now we can calculate Lucy’s age using Equation 3. If Lucy is 2 years older than Max, Lucy must be 8.

Answer: 8

Another method that could be used to solve this problem is bar modelling.