# Creating and Manipulating Algebraic Expressions - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Creating and Manipulating Algebraic Expressions.

Printable worksheets containing selections of these problems are available here:

 Stage 3 ★ Sheet 1 Solutions

### Stamp Collecting

##### KS 3 Short Challenge Level:

Weekly Problem 28 - 2016
Last week, Tom and Sophie bought some stamps for their collections. Each stamp Tom bought cost him £1.10, whilst Sophie paid 70p for each of her stamps. Between them they spent exactly £10. How many stamps did they buy in total?

### Punky Fish

##### KS 3 Short Challenge Level:

Weekly Problem 12 - 2008
A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?

### Inspector Remorse

##### KS 3 Short Challenge Level:

Weekly Problem 49 - 2011
How long will it take Inspector Remorse to crack this crime spree?

### Paul's Children

##### KS 3 Short Challenge Level:

Weekly Problem 29 - 2016
Paul is 32 years old. In ten years time, Paul's age will be the sum of the ages of his three sons. What do the ages of his sons add up to at present?

### Multiple Magic

##### KS 3 Short Challenge Level:

Weekly Problem 31 - 2009
Think of any whole number. Each time you perform a sequence of operations on it, what do you notice about the divisors of your answer?

### No Matter

##### KS 3 Short Challenge Level:

Weekly Problem 2 - 2013
After performing some operations, what number is your answer always a multiple of?

##### KS 3 Short Challenge Level:

Weekly Problem 52 - 2016
Find four integers whose sum is 400 and such that the first integer is equal to twice the second integer, three times the third integer and four times the fourth integer.

### The Square of My Age

##### KS 3 Short Challenge Level:

Weekly Problem 34 - 2011
Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

### Forming Groups

##### KS 3 Short Challenge Level:

Weekly Problem 34 - 2006
Seventy pupils are divided into two groups. Can you work out the differnece between the number of boys in group 1 and the number of girls in group 2?

### Crossover

##### KS 3 Short Challenge Level:

Weekly Problem 14 - 2017
The numbers 2 up to 8 are to be placed in the diagram on the right such that the row and column add up to 21. Which numbers can replace x?

### Square Total

##### KS 3 Short Challenge Level:

Weekly Problem 13 - 2017
Anastasia thinks of a number. Each of her friends performs an operation on it. The total of these is a square number. What is the smallest number Anastasia could have thought of?

### Building Up

##### KS 3 Short Challenge Level:

Weekly Problem 16 - 2015
In the diagram, the number in each box is obtained by adding the two immediately below. What is the number in the top box?

### Cube Pile

##### KS 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?

### How Many Rectangles?

##### KS 3 Short Challenge Level:

Weekly Problem 37 - 2016
By drawing 5 horizontal and four vertical lines, one can form 12 rectangles. What is the greatest number of rectangles that can be formed by drawing 15 lines?

### Kangaroo Subtraction

##### KS 3 Short Challenge Level:

Weekly Problem 2 - 2010
Can you solve this 'KANGAROO' alphanumeric subtraction?

### 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?

### Beans Eating Beans

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 13 - 2007
The Bean family are very particular about beans. At every meal all Beans eat some beans... At their last meal they ate 23 beans altogether. How many beans did Pa Bean eat?

### Nine in a Line

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 9 - 2008
The sum of 9 consecutive positive whole numbers is 2007. What is the largest of these numbers?

### Largest Expression

##### KS 4 Short Challenge Level:

Weekly Problem 36 - 2006
Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?