# Equations and Formulae Stage 3 - Short Problems

### Star Sum

##### Stage: 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?

### Partial Magic

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

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

### Weekly Problem 33 - 2008

##### Short Challenge Level:

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

### Debt Recovery

##### Stage: 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?

### Average Surroundings

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

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

### Weekly Problem 48 - 2009

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

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.

### Seven Dwarfs

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

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

### Sum = Product = Quotient

##### Stage: 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?

##### Stage: 2 and 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.

### Don't Be Late

##### Stage: 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.

### Symbol

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

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

### In Sum-mary

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

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

### Alien Currency

##### Stage: 3 and 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?

### Algebraic Differences

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

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

### Shilling Tuppence

##### Stage: 3 and 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?

### Shape Sums

##### Stage: 3 Short Challenge Level:

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

### Turnips

##### Stage: 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?

##### Stage: 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?

### Between a Square and a Cube

##### Stage: 3 Short Challenge Level:

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

### Nine, Ten and One

##### Stage: 3 Short Challenge Level:

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

### Day of the Triffids

##### Stage: 3 Short Challenge Level:

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

### Fractions of Fractions

##### Stage: 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?

### Magic Octahedron

##### Stage: 3 Short Challenge Level:

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

### Packing Boxes

##### Stage: 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.

### Square and Cube

##### Stage: 3 and 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?

### Granny's Age

##### Stage: 3 and 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

##### Stage: 3 and 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?

### Magic 7

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

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

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

Weekly Problem 48 - 2015
Miss Quaffley's class went to the library. If you know how many books each boy, girl and teddy bear took out, can you work out how many girls there are?

### Dean's Mountain

##### Stage: 3 and 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?

### Hillwalking

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

Weekly Problem 40 - 2016
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?

### Traffic Jam

##### Stage: 3 Short Challenge Level:

Weekly Problem 1 - 2017
Yesterday evening, Emily's journey home took 25% longer than usual. By what percentage was her average speed reduced compared to normal?

### Triangular Algebra

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

Weekly Problem 26 - 2017
The angles in the triangle are shown in the diagram in terms of x and y. If x and y are positive integers, what is the value of x+y?

### Equal Means

##### Stage: 3 Short Challenge Level:

Weekly Problem 36 - 2017
What value of x makes the mean of the first three numbers in this list equal to the mean of the other four?

### Bookshop

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

Weekly Problem 3 - 2017
Books cost £3.40 and magazines cost £1.60. If Clara spends £23 on books and Magazines, how many of each does she buy?

### Oldest and Youngest

##### Stage: 3 Short Challenge Level:

Weekly Problem 11 - 2017
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?

### Corner Cut

##### Stage: 3 Short Challenge Level:

Weekly Problem 23 - 2017
Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle. What is the side length of the small triangles?

### Cube Pile

##### Stage: 3 Short Challenge Level:

Weekly Problem 29 - 2017
Rick has five cubes. Each one is 2cm taller than the previous one. The largest cube is the same height as a tower built of the two smallest cubes. How high would a tower of all five cubes be?

### Tennis Training

##### Stage: 3 Short Challenge Level:

Weekly Problem 40 - 2017
After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?

### Helen's Family

##### Stage: 3 Short Challenge Level:

Weekly Problem 42 - 2017
Helen has twice as many sisters as brothers. Her brother Tim has three times as many sisters as brothers. How many children are there in the family?