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Broad Topics > Information and Communications Technology > smartphone

Sweet Shop

Stage: 3 Challenge Level:

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

Letter Land

Stage: 3 Challenge Level:

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.

One and Three

Stage: 4 Challenge Level:

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

Children at Large

Stage: 3 Challenge Level:

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

Summing Consecutive Numbers

Stage: 3 Challenge Level:

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Consecutive Numbers

Stage: 2 and 3 Challenge Level:

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Make 37

Stage: 2 and 3 Challenge Level:

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Fair Shares?

Stage: 4 Challenge Level:

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

Special Numbers

Stage: 3 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?

Terminology

Stage: 4 Challenge Level:

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

Consecutive Negative Numbers

Stage: 3 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Marbles in a Box

Stage: 3 Challenge Level:

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

Squares in Rectangles

Stage: 3 Challenge Level:

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Weights

Stage: 3 Challenge Level:

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Sissa's Reward

Stage: 3 Challenge Level:

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

CD Heaven

Stage: 4 Challenge Level:

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

Counting Factors

Stage: 3 Challenge Level:

Is there an efficient way to work out how many factors a large number has?

Repetitiously

Stage: 3 Challenge Level:

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

Always Perfect

Stage: 4 Challenge Level:

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

What's it Worth?

Stage: 3 and 4 Challenge Level:

There are lots of different methods to find out what the shapes are worth - how many can you find?

Matchless

Stage: 4 Challenge Level:

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

M, M and M

Stage: 3 Challenge Level:

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

Differences

Stage: 3 Challenge Level:

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Picturing Square Numbers

Stage: 3 Challenge Level:

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Difference Sudoku

Stage: 4 Challenge Level:

Use the differences to find the solution to this Sudoku.

1 Step 2 Step

Stage: 3 Challenge Level:

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Litov's Mean Value Theorem

Stage: 3 Challenge Level:

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Dozens

Stage: 2 and 3 Challenge Level:

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

Searching for Mean(ing)

Stage: 3 Challenge Level:

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

Product Sudoku

Stage: 3 Challenge Level:

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

Can They Be Equal?

Stage: 3 Challenge Level:

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Perfectly Square

Stage: 4 Challenge Level:

The sums of the squares of three related numbers is also a perfect square - can you explain why?

Handshakes

Stage: 3 Challenge Level:

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

Stage: 3 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. . . .

Mirror, Mirror...

Stage: 3 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

Who Is the Fairest of Them All ?

Stage: 3 Challenge Level:

Explore the effect of combining enlargements.

Eight Hidden Squares

Stage: 2 and 3 Challenge Level:

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

The Spider and the Fly

Stage: 4 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?

Stage: 3 Challenge Level:

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

Route to Infinity

Stage: 3 Challenge Level:

Can you describe this route to infinity? Where will the arrows take you next?

Tet-trouble

Stage: 4 Challenge Level:

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

Areas of Parallelograms

Stage: 4 Challenge Level:

Can you find the area of a parallelogram defined by two vectors?

2-digit Square

Stage: 4 Challenge Level:

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Fence It

Stage: 3 Challenge Level:

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Nicely Similar

Stage: 4 Challenge Level:

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

Attractive Rotations

Stage: 3 Challenge Level:

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Days and Dates

Stage: 3 Challenge Level:

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

How Much Can We Spend?

Stage: 3 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?

Thousands and Millions

Stage: 3 Challenge Level:

Here's a chance to work with large numbers...

Consecutive Seven

Stage: 3 Challenge Level:

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?