Equations and Formulae Stage 3 - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Equations and Formulae - Stage 3.

Currency Exchange

KS 2 & 3 Short Challenge Level:

Weekly Problem 48 - 2009
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.

In Sum-mary

KS 2 & 3 Short Challenge Level:

Weekly Problem 14 - 2011
What does the sum of these three numbers tell us about their product?

Seven Dwarfs

KS 2 & 3 Short Challenge Level:

Weekly Problem 13 - 2010
The Seven Dwarfs have seven different birthdays. How old can they be?

KS 2 & 3 Short Challenge Level:

Weekly Problem 16 - 2010
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.

Turnips

KS 3 Short Challenge Level:

Weekly Problem 37 - 2012
Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?

To Run or Not to Run?

KS 3 Short Challenge Level:

Weekly Problem 38 - 2012
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?

Packing Boxes

KS 3 Short Challenge Level:

Weekly Problem 28 - 2011
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.

Sum = Product = Quotient

KS 3 Short Challenge Level:

Weekly Problem 15 - 2010
Can you find a pair of numbers such that their sum, product and quotient are all equal? Are there any other pairs?

Three Fruits

KS 3 Short Challenge Level:

Weekly Problem 33 - 2008
Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?

Between a Square and a Cube

KS 3 Short Challenge Level:

Weekly Problem 51 - 2011
The equation $x^2+2=y^3$ looks nearly quadratic. What integer solutions can you find?

Debt Recovery

KS 3 Short Challenge Level:

Weekly Problem 7 - 2009
Tony and Tina can't work out which of them owes what to the other. Can you?

Nine, Ten and One

KS 3 Short Challenge Level:

Weekly Problem 3 - 2013
Can you find the value of t in these equations?

Don't Be Late

KS 3 Short Challenge Level:

Weekly Problem 31 - 2010
Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

Shape Sums

KS 3 Short Challenge Level:

Weekly Problem 22 - 2016
Given some relationships amongst these shapes, how many triangles equal one diamond?

Fractions of Fractions

KS 3 Short Challenge Level:

Weekly Problem 44 - 2013
If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?

Star Sum

KS 3 Short Challenge Level:

Weekly Problem 40 - 2011
You may have seen magic squares before, but can you work out the missing numbers on this magic star?

Magic Octahedron

KS 3 Short Challenge Level:

Weekly Problem 20 - 2010
You have already used Magic Squares, now meet a Magic Octahedron...

Day of the Triffids

KS 3 Short Challenge Level:

Weekly Problem 23 - 2013
Jasmine buys three different types of plant. How many triffids did she buy?

Granny's Age

KS 3 & 4 Short Challenge Level:

Weekly Problem 10 - 2015
Granny is four times as old as I am. Five years ago she was five times as old as I was. What is the sum of our ages?

Five-to

KS 3 & 4 Short Challenge Level:

Weekly Problem 22 - 2015
The number 2005 is the sum of a sequence of five consecutive positive integers. What is the smallest of these integers?

Exactly Three-quarters

KS 3 & 4 Short Challenge Level:

Weekly Problem 30 - 2007
Three-quarters of the area of the rectangle has been shaded. What is the length of x?

Magic 7

KS 3 & 4 Short Challenge Level:

Weekly Problem 36 - 2015
Can you complete this magic square with the numbers from 7 to 15?

Monetary Difference

KS 3 & 4 Short Challenge Level:

Weekly Problem 50 - 2007
Al, Berti, Chris and Di have sums of money totalling £150... What is the difference between the amount Al and Di have?

Alien Currency

KS 3 & 4 Short Challenge Level:

Weekly Problem 22 - 2014
The planet Zog has both green and blue banknotes. Can you work out how many zogs two green banknotes and three blue banknotes are worth?

Partial Magic

KS 3 & 4 Short Challenge Level:

Weekly Problem 41 - 2011
This magic square has only been partially completed. Can you still solve it...

Square and Cube

KS 3 & 4 Short Challenge Level:

Weekly Problem 24 - 2014
The square of a positive number is twice as big as the cube of that number. What is the number?

Dean's Mountain

KS 3 & 4 Short Challenge Level:

Weekly Problem 20 - 2016
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?

Algebraic Differences

KS 3 & 4 Short Challenge Level:

Weekly Problem 42 - 2014
If $6x−y=21$ and $6y−x=14$, what is the value of $x−y$?

Average Surroundings

KS 3 & 4 Short Challenge Level:

Weekly Problem 15 - 2009
Can you work out Ali's age based on the diagram?

Shilling Tuppence

KS 3 & 4 Short Challenge Level:

Weekly Problem 50 - 2014
Cheryl finds a bag of coins. Can you work out how many more 5p coins than 2p coins are in the bag?

Symbol

KS 3 & 4 Short Challenge Level:

Weekly Problem 2 - 2011
Using the new operator $\oplus$, can you solve this equation?