A collection of short problems on Angles, Polygons and Geometrical Proof.

A collection of short problems on Pythagoras's Theorem and Trigonometry.

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?

Weekly Problem 38 - 2017

In the diagram, what is the value of $x$?

Can you work out the values of J, M and C in this sum?

Weekly Problem 8 - 2016

Can you work out the size of the angles in a quadrilateral?

Fill in the grid with A-E like a Sudoku. Which letter is in the starred square?

Weekly Problem 39 - 2016

In the diagram, VWX and XYZ are congruent equilateral triangles. What is the size of angle VWY?

Mr Ross tells truths or lies depending on the day of the week. Can you catch him out?

The 30 students in a class have 25 different birthdays between them. What is the largest number that can share any birthday?

Weekly Problem 32 - 2015

Can you work out the missing numbers in this multiplication magic square?

In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?

You may have met Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different - can you still solve it?

Can you work out the number of chairs at a cafe from the number of legs?

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?

If it takes 852 digits to number all the pages of a book, what is the number of the last page?

If Clara spends £23 on books and magazines, how many of each does she buy?

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?

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?

Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?

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?

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?

Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?

Weekly Problem 47 - 2017

How many numbers do I need in a list to have two squares, two primes and two cubes?

Weekly Problem 41 - 2016

The diagram shows a square, with lines drawn from its centre. What is the shaded area?

When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?

Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?