Reasoning, Justifying, Convincing and Proof - Short Problems
Angles, Polygons and Geometrical Proof Short Problems
A collection of short problems on Angles, Polygons and Geometrical Proof.
Pythagoras' Theorem and Trigonometry - Short Problems
A collection of short problems on Pythagoras's Theorem and Trigonometry.
Weekly Lies
Mr Ross tells truths or lies depending on the day of the week. Can you catch him out?
Equilateral Pair
Weekly Problem 39 - 2016
In the diagram, VWX and XYZ are congruent equilateral triangles. What is the size of angle VWY?
Distinct Diagonals
Weekly Problem 21 - 2010
How many diagonals can you draw on this square...
Multiplication Magic Square
Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?
Quiz Questions
Jack does a 20-question quiz. How many questions didn't he attempt?
Kept Apart
The squares of this grid contain one of the letters P, Q, R and S. Can you complete this square so that touching squares do not contain the same letter? How many possibilities are there?
Shared Vertex
Weekly Problem 38 - 2017
In the diagram, what is the value of $x$?
Out of Line
Fill in the grid with A-E like a Sudoku. Which letter is in the starred square?
Down and Along
Can you work out the values of J, M and C in this sum?
Other Side
Weekly Problem 8 - 2016
Can you work out the size of the angles in a quadrilateral?
Birthday Party
The 30 students in a class have 25 different birthdays between them. What is the largest number that can share any birthday?
Digital Book
If it takes 852 digits to number all the pages of a book, what is the number of the last page?
So Many Sums
In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?
Anti-magic Square
You may have met Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different - can you still solve it?
A Leg to Stand On
Can you work out the number of chairs at a cafe from the number of legs?
Bookshop
If Clara spends £23 on books and magazines, how many of each does she buy?
Total Totality
Is it possible to arrange the numbers 1-6 on the nodes of this diagram, so that all the sums between numbers on adjacent nodes are different?
Distinct in a Line
This grid can be filled so that each of the numbers 1, 2, 3, 4, 5 appears just once in each row, column and diagonal. Which number goes in the centre square?
Knights and Knaves
Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?
More Total Totality
Is it possible to arrange the numbers 1-6 on the nodes of this diagram, so that all the sums between numbers on adjacent nodes are different?
Peter's Primes
Peter wrote a list of all the numbers that can be formed by changing one digit of the number 200. How many of Peter's numbers are prime?
Shaded Square
Weekly Problem 41 - 2016
The diagram shows a square, with lines drawn from its centre. What is the shaded area?
Spot the Fake
One of N coins is slightly heavier than the others. How large can N be if the coin can be determined with only two weighings with a set of scales?
Takeaway Time
Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?
Long List
Weekly Problem 47 - 2017
How many numbers do I need in a list to have two squares, two primes and two cubes?
Square LCM
Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?
Digital Counter
When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?
Triangular Intersection
What is the largest number of intersection points that a triangle and a quadrilateral can have?
Curve Fitter
This problem challenges you to find cubic equations which satisfy different conditions.
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Seven Squares - Group-worthy Task
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?