Challenge Level

Luis writes down eight consecutive positive integers. The sum of the three smallest numbers is 33. What is the sum of the three largest numbers?

Challenge Level

Given some relationships amongst these shapes, how many triangles equal one diamond?

Challenge Level

The Seven Dwarfs have seven different birthdays. How old can they be?

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The number 2005 is the sum of a sequence of five consecutive positive integers. What is the smallest of these integers?

Challenge Level

This magic square has only been partially completed. Can you still solve it...

Challenge Level

What number could replace * so that */5 is between 3 and 4?

Challenge Level

Cheryl finds a bag of coins. Can you work out how many more 5p coins than 2p coins are in the bag?

Challenge Level

Using the new operator $\oplus$, can you solve this equation?

Challenge Level

Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?

Challenge Level

The numbers 2 to 8 are to be placed in the diagram so that the row and column each adds to 21. Which numbers can replace x?

Challenge Level

You may have seen magic squares before, but can you work out the missing numbers on this magic star?

Challenge Level

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

Challenge Level

Each interior angle in a quadrilateral (apart from the smallest) is twice the previous one. What is the size of the smallest interior angle?

Challenge Level

If an athlete takes 10 minutes longer to walk, run and cycle three miles than he does to cycle all three miles, how long does it take him?

Challenge Level

Can you complete this magic square with the numbers from 7 to 15?

Challenge Level

Can you find the solution to this equation? Each of the different letters stands for a different number.

Challenge Level

Can you find the sum of all of the numbers in the table?

Challenge Level

In a 7-digit numerical code, each group of four consecutive digits adds to 16, and each group of five consecutive digits adds to 19. What is the sum of all 7 digits?

Challenge Level

Can you sum up the solutions to this equation?

Challenge Level

For how many positive values of $n$ are both $\frac n2$ and $2n$ three-digit whole numbers?

Challenge Level

Can you work out the product of $a$ and $b$ from the information in the question?

Challenge Level

Weighing the baby at the clinic was a problem. Can you work out the total weight of the baby, the nurse and me from the information given?

Challenge Level

Each row and column has the total given. What is the value of the heart symbol?

Challenge Level

Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?

Challenge Level

Jasmine buys three different types of plant. How many triffids did she buy?

Challenge Level

Can you work out how many spheres will balance a single pyramid?

Challenge Level

Kevin has moved some tiles to change the shape of his patio from a square to a rectangle. What are the lengths of the sides of the rectangle?

Challenge Level

If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?

Challenge Level

Can you work out Ali's age based on the diagram?

Challenge Level

There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?

Challenge Level

A table has blocks of wood placed on and next to it. Can you work out how tall it is?

Challenge Level

Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.

Challenge Level

Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into three pieces in order to weigh it...

Challenge Level

Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

Challenge Level

Can you find a pair of numbers such that their sum, product and quotient are all equal? Are there any other pairs?

Challenge Level

If $a \times b=2$, $b \times c=24$, $c \times a=3$ and $a$, $b$ and $c$ are positive, what is the value of $a+b+c$?

Challenge Level

Can you work out the angles of a triangle from the relationships between them?

Challenge Level

The planet Zog has both green and blue bank notes. Can you work out how many zogs two green and three blue bank notes are worth?

Challenge Level

After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?

Challenge Level

Manipulate one algebraic fraction to solve another.

Challenge Level

Al, Bertie, Chris and Di have sums of money totalling Â£150... What is the difference between the amount Al and Di have?

Challenge Level

If $6xâˆ’y=21$ and $6yâˆ’x=14$, what is the value of $xâˆ’y$?

Challenge Level

If you know how many books each boy, girl and teddy bear borrowed from the library, can you work out the number of girls?

Challenge Level

Can you find the value of this expression, which contains infinitely nested square roots?

Challenge Level

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?