Creating and Manipulating Algebraic Expressions - Short Problems

Gender Balance

Stage: 3 Short Challenge Level:

Weekly Problem 36 - 2012
Can you work out how many more boys are in group 1 than girls are in group 2?

Integer and Integer

Stage: 3 Short Challenge Level:

Weekly Problem 39 - 2012
For how many values of $n$ are both $n$ and $\frac{n+3}{n−1}$ integers?

Inspector Remorse

Stage: 3 Short Challenge Level:

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

Four or Five

Stage: 3 Short Challenge Level:

Weekly Problem 19 - 2012
The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?

Siblings

Stage: 2 and 3 Short Challenge Level:

Weekly Problem 17 - 2013
Anna has 3 brothers and 5 sisters. What is the product of the number of brothers and number of sisters that her brother Tom has?

No Matter

Stage: 3 Short Challenge Level:

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

Stage: 3 Short Challenge Level:

Weekly Problem 35 - 2013
The hour hand on the Mad Hatter's watch moves normally, but the minute hand moves too fast! When will it next show the correct time?

Weekly Problem 43 - 2008

Stage: 3 Short Challenge Level:

A knitted scarf uses three balls of wool. How many balls of wool do I have at the end of the day?

Refuelling

Stage: 3 Short Challenge Level:

Weekly Problem 12 - 2009
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 31 - 2009

Stage: 3 Short Challenge Level:

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?

Kangaroo Subtraction

Stage: 2 and 3 Short Challenge Level:

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

Reciprocal Values

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 28 - 2010
Manipulate one algebraic fraction to solve another.

The Square of My Age

Stage: 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?

Repeat Product

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 3 - 2014
Can you work out the value of P+Q+R in the multiplication shown?

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?

Relative Time

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 25 - 2014
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?

Pyramidal N-gon

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 43 - 2014
The base of a pyramid has n edges. What is the difference between the number of edges the pyramid has and the number of faces the pyramid has?

Building Up

Stage: 3 and 4 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?

Divide and Conquer

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 23 - 2015
Can you simplify this algebraic expression with many divisions?

Stamp Collecting

Stage: 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?

Paul's Children

Stage: 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?

How Many Rectangles?

Stage: 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?

Stage: 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.

Crossover

Stage: 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

Stage: 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?

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?