Being Resilient is part of our Developing Mathematical Habits of Mind collection.
Good thinkers are resilient. They don't give up easily, and are motivated to work hard and keep going when faced with challenges. They recognise that we all fail sometimes, and when this happens, they bounce back and try alternative approaches. Find out more in What Does it Feel Like to Do Maths, which includes a film of the mathematician Andrew Wiles talking about his
personal experience of seeking a proof of Fermat's Last Theorem.
Want to become a more resilient mathematician?
These problems may require you to persevere when the solutions are not immediately obvious. Take a look, we hope you'll stick with them and feel a sense of achievement at the end!
You can browse through the Number, Algebra, Geometry or Statistics collections, or scroll down to see the full set of problems below.





Factors and multiples game
A game in which players take it in turns to choose a number. Can you block your opponent?


Number lines in disguise

Factor lines
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Got it
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Two and two
How many solutions can you find to this sum? Each of the different letters stands for a different number.



Can you make 100?

Number daisy

American billions

Frogs

Reflecting squarely
In how many ways can you fit all three pieces together to make shapes with line symmetry?

Isosceles triangles


Substitution cipher

Factors and multiples puzzle

M, M and M
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Elevenses

Charlie's delightful machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Last biscuit
Can you find a strategy that ensures you get to take the last biscuit in this game?

Wipeout

Funny factorisation


Where can we visit?

Same length
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Squares in rectangles

Product Sudoku
The clues for this Sudoku are the product of the numbers in adjacent squares.

Tower of Hanoi
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Nine colours

Shopping basket
The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Triangles to tetrahedra

Cuboids


A little light thinking
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

In a box

Partly painted cube

Kite in a square
Can you make sense of the three methods to work out what fraction of the total area is shaded?

