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Deputy First Minister's Summer Maths Challenge 2019

If you want something fun to keep them busy these holidays, why not try the Deputy First Minister's Maths Challenge? It's full of puzzles you can pick and choose from to keep them entertained.

You can get all the workings and solutions here.

Puzzle 1: Family Archery Challenge

On your marks...

archery board

On their Summer holiday, the Archer family go to an archery activity and compete against each other. Based on the target scoreboard above, can you work out the following puzzles:

All of the arrows land on the board and each round has 4 arrows.

Round 1 – Mum scores 54, Dad scores 55, Iona scores 70 and Harris scores 58. Suggest how each family member might have scored with their arrows to get their total.

Round 2 – Each member of the family scores the same total with their 4 arrows. Can you find a total where they managed this with different combinations of arrows? Scores on the target board can be used more than once.

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Bonus round!

There's a sign offering anyone that scores over 60 with 3 arrows another game free. How many possibilities can you come up with for this, and what are they?

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Why not create your own game by making a target board and throwing coins or counters? You can keep your maths skills sharp by working out the scores. Can you get a bullseye?

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Puzzle 2: Summer holiday packing

How many outfits?



Iona has packed 3 different t-shirts, 3 different pairs of shoes and 3 different pairs of leggings in her rucksack. How many different outfits can she make?

Can you explain how you worked it out?

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Puzzle 3: Puzzle book

You're the referee

soccer algebra

Iona and Harris can't agree on the correct answer to the puzzle. Iona thinks it's 68 but Harris does not. What do you think is the correct answer? Can you explain this for Iona and Harris?

Can you and some of your family do this by yourselves and then compare your answers? Did you all get the same answers?

If not, discuss your thinking and listen to each others' explanations. Who is right and why?

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Puzzle 4: Scotland Team Activity

Favourite players

Women's soccer team

The family are talking about their favourite players from the Scottish Women’s Football Team World Cup 2019 squad. They have turned this into a guessing game and are giving each other clues to help them find the player.

Can you find the name of each family member’s favourite player?


  • she plays for a Scottish team
  • her caps and age are both even numbers
  • her goals scored is 3²


  • her goals scored total is a prime number
  • she is a Forward
  • the total of her age, caps and goals scored is a multiple of ten


  • her age is 1/4 of 100
  • she has not yet scored any goals
  • her number of caps can be divided equally by 17 and 2


  • the total of all three statistics is even
  • she is in her 20s
  • she has one clean sheet

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Super fan!

favourite player

Can you create a set of clues about your favourite player for a friend to solve?

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Puzzle 5: Shape task

How many triangles can you see?



Iona and Harris are looking for another puzzle in their book. Iona loves shape puzzles.

Harris thinks the answer to the question is 26 but Iona thinks Harris is wrong. Who is right and why?

When looking for triangles, Harris spotted lots of other shapes. How many different shapes can you find? Look carefully, not all shapes are obvious at first glance!

The puzzle contains more shapes than triangles as you’ve probably noticed – what do you know about these shapes – for example, their names, how many lines they have, are they symmetrical? What else?

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Want more ideas for fun with numbers?

Tips for family fun

  • Play board games! Games can involve a lot of maths: this could be counting squares, looking for sequences, moving in different directions, exploring probability by rolling dice or being dealt a card, and following logic and rules.
  • Play puzzles and puzzle-like games. Examples include Noughts and Crosses, Guess Who?, Sudoku, Dominoes, Battleships, Dots-and-Boxes and Chess. These involve strategic thinking, problem solving, and planning, as well as lots of the skills mentioned above.
  • Include your kids in everyday activities that use maths. For instance cooking often asks for lots of quantities and measuring as well as shapes, times and temperatures. We have loads of cheap yummy recipes that are easy enough for kids to help you make.
  • Shopping involves prices, counting money, and checking the time.
  • Estimate all sorts of things together: “I wonder how many steps there are here?”
  • Plan journeys together, look at maps, timetables, and talk about distances.
  • Talk about maths in a positive way, that way your child will too!
  • Check out Parentzone Scotland at

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Download the challenge

Gaelic & English versions

  • Download the Gaelic version here
  • Download the English version here

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Last updated: 6 Jan, 2020