Equations and Formulae Stage 3 - Short Problems

A collection of short Stage 3 problems on equations and formulae



Weekly Problem 40 - 2011

Challenge Level: Challenge Level:1

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

Weekly Problem 41 - 2011

Challenge Level: Challenge Level:1

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

Weekly Problem 49 - 2011

Challenge Level: Challenge Level:1

How long will it take Inspector Remorse to crack this crime spree?

Weekly Problem 33 - 2008

Short Challenge Level: Challenge Level:1

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

Weekly Problem 36 - 2008

Stage: 3 Short Challenge Level: Challenge Level:1

Weighing the baby at the clinic was a problem. The baby would not keep still so we had to hold her while on the scales. Can you work out our combined weight?

Weekly Problem 7 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

Tony and Tina can't work out which of them owes what to the other. Can you?

Weekly Problem 12 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

A car can go r miles on s gallons of petrol. How many gallons of petrol would it need for a journey of t miles?

Weekly Problem 15 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 48 - 2009

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Dan and Ann have 9 and 8 coins respectively. What is the smallest number of coins they must swap so they end up with equal amounts of money.

Weekly Problem 13 - 2010

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 15 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 16 - 2010

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Is it wise for Jane to use this certain method for choosing her padlock code? Try to work out all possible combinations she might use.

Weekly Problem 31 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

Weekly Problem 2 - 2011

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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

Weekly Problem 14 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

What does the sum of these three numbers tell us about their product?

Weekly Problem 33 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 22 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 22 - 2014

Weekly Problem 42 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 42 - 2014

Weekly Problem 50 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 50 - 2014

Weekly Problem 22 - 2016

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 20 - 2016

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Dean runs up a mountain road at 8 km per hour. It takes him one hour to get to the top. He runs down the same mountain at 12 km per hour. How long does it take him to run down the mountain?

Weekly Problem 40 - 2016

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

Andrew walks along a flat path, then up and down a hill, then back along the path. Is it possible to work out how far he has walked?

Weekly Problem 1 - 2017

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Yesterday evening, Emily's journey home took 25% longer than usual. By what percentage was her average speed reduced compared to normal?