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Broad Topics > Habits of Mind > Resourceful Multiplication Arithmagons

Age 14 to 16 Challenge Level:

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons? Arithmagons

Age 14 to 16 Challenge Level:

Can you find the values at the vertices when you know the values on the edges? A Little Light Thinking

Age 14 to 16 Challenge Level:

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights? Tower of Hanoi

Age 11 to 14 Challenge Level:

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

Age 14 to 16 Challenge Level:

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays? Frogs

Age 11 to 14 Challenge Level:

How many moves does it take to swap over some red and blue frogs? Do you have a method? Attractive Tablecloths

Age 14 to 16 Challenge Level:

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs? How Much Can We Spend?

Age 11 to 14 Challenge Level:

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know? Marbles in a Box

Age 11 to 16 Challenge Level:

How many winning lines can you make in a three-dimensional version of noughts and crosses? Special Numbers

Age 11 to 14 Challenge Level:

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be? Which Solids Can We Make?

Age 11 to 14 Challenge Level:

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids? Reversals

Age 11 to 14 Challenge Level:

Where should you start, if you want to finish back where you started? Unequal Averages

Age 11 to 14 Challenge Level:

Play around with sets of five numbers and see what you can discover about different types of average... A Chance to Win?

Age 11 to 14 Challenge Level:

Imagine you were given the chance to win some money... and imagine you had nothing to lose... Where Can We Visit?

Age 11 to 14 Challenge Level:

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think? Age 11 to 14 Challenge Level:

How many different symmetrical shapes can you make by shading triangles or squares? On the Edge

Age 11 to 14 Challenge Level:

If you move the tiles around, can you make squares with different coloured edges? Age 11 to 14 Challenge Level:

What happens when you add a three digit number to its reverse? Semi-regular Tessellations

Age 11 to 16 Challenge Level:

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations? Triangles to Tetrahedra

Age 11 to 14 Challenge Level:

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make? Treasure Hunt

Age 7 to 14 Challenge Level:

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses? Constructing Triangles

Age 11 to 14 Challenge Level:

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw? Age 11 to 14 Challenge Level:

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . . Gabriel's Problem

Age 11 to 14 Challenge Level:

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was? Charlie's Delightful Machine

Age 11 to 16 Challenge Level:

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

Age 7 to 14 Challenge Level:

Do you know a quick way to check if a number is a multiple of two? How about three, four or six? Nice or Nasty

Age 7 to 14 Challenge Level:

There are nasty versions of this dice game but we'll start with the nice ones... Difference Sudoku

Age 14 to 16 Challenge Level:

Use the differences to find the solution to this Sudoku. Funny Factorisation

Age 11 to 14 Challenge Level:

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors? Shifting Times Tables

Age 11 to 14 Challenge Level:

Can you find a way to identify times tables after they have been shifted up or down? Stars

Age 11 to 14 Challenge Level:

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit? Cosy Corner

Age 11 to 14 Challenge Level:

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning? Two's Company

Age 11 to 14 Challenge Level:

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning? Cryptarithms

Age 11 to 14 Challenge Level:

Can you crack these cryptarithms? Two and Two

Age 11 to 14 Challenge Level:

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

Age 14 to 16 Challenge Level:

Can you find the hidden factors which multiply together to produce each quadratic expression? Cuboids

Age 11 to 14 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all? Last One Standing

Age 14 to 16 Challenge Level:

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row? Odds and Evens

Age 11 to 14 Challenge Level:

Are these games fair? How can you tell? What Does Random Look Like?

Age 11 to 14 Challenge Level:

Engage in a little mathematical detective work to see if you can spot the fakes. Sociable Cards

Age 11 to 14 Challenge Level:

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up? Substitution Cipher

Age 11 to 14 Challenge Level:

Find the frequency distribution for ordinary English, and use it to help you crack the code. Which Spinners?

Age 14 to 18 Challenge Level:

Can you work out which spinners were used to generate the frequency charts? Wipeout

Age 11 to 14 Challenge Level:

Can you do a little mathematical detective work to figure out which number has been wiped out? Dicey Operations

Age 11 to 14 Challenge Level:

Who said that adding, subtracting, multiplying and dividing couldn't be fun? M, M and M

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw? Transformation Game

Age 11 to 14 Challenge Level:

Why not challenge a friend to play this transformation game? Hexy-metry

Age 14 to 16 Challenge Level:

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle? The Spider and the Fly

Age 14 to 16 Challenge Level:

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?