Explaining, convincing and proving

problem

Kept Apart

Age

11 to 14

Challenge level

1 out of 3

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?
problem

Would You Like a Jelly Baby?

Age

11 to 14

Challenge level

1 out of 3

What is the smallest number of jelly babies Tom must take, to be certain that he gets at least one of each flavour?
problem

Multiplication Magic Square

Age

11 to 14

Challenge level

1 out of 3

Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?
problem

Down and Along

Age

11 to 14

Challenge level

1 out of 3

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

Other Side

Age

11 to 14

Challenge level

1 out of 3

Weekly Problem 8 - 2016
Can you work out the size of the angles in a quadrilateral?
problem

Equilateral Pair

Age

11 to 14

Challenge level

1 out of 3

Weekly Problem 39 - 2016
In the diagram, VWX and XYZ are congruent equilateral triangles. What is the size of angle VWY?
problem

What's on the Back?

Age

11 to 14

Challenge level

1 out of 3

Four cards have a number on one side and a phrase on the back. On each card, the number does not have the property described on the back. What do the four cards have on them?
problem

Shared Vertex

Age

11 to 14

Challenge level

1 out of 3

Weekly Problem 38 - 2017
In the diagram, what is the value of $x$?
problem

Anti-Magic Square

Age

11 to 14

Challenge level

2 out of 3

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

Marbles

Age

11 to 14

Challenge level

2 out of 3

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?