What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

In this problem, we're going to find sets of letter shapes that go together.

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

An investigation that gives you the opportunity to make and justify predictions.

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

Can you decode the mysterious markings on this ancient bone tool?

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

What information helped medical pioneers decide on the cause of a disease? Especially in a time before microscopes were as powerful as they are today ?

I need a figure for the fish population in a lake, how does it help to catch and mark 40 fish ?

Can you make a hypothesis to explain these ancient numbers?

Points D, E and F are on the the sides of triangle ABC. Circumcircles are drawn to the triangles ADE, BEF and CFD respectively. What do you notice about these three circumcircles?

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

The circumcentres of four triangles are joined to form a quadrilateral. What do you notice about this quadrilateral as the dynamic image changes? Can you prove your conjecture?

A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.

If you plot these graphs they may look the same, but are they?

When does a pattern start to exhibit structure? Can you crack the code used by the computer?

Jake and Ellie approached this problem in a similar way and have explained clearly what they did.

A good visualisation can be really useful when we need to convince ourselves that a probability calculation is correct. Here's a nice one.

We had various suggestions of ways to describe these patterns. We saw a good mixture of analysis and experiment in the solutions

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.