Can you make matrices which will fix one lucky vector and crush another to zero?
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
When does a pattern start to exhibit structure? Can you crack the
code used by the computer?
Look for the common features in these graphs. Which graphs belong together?
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Can you find the values at the vertices when you know the values on the edges?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Which of these triangular jigsaws are impossible to finish?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Which of these roads will satisfy a Munchkin builder?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
A polite number can be written as the sum of two or more
consecutive positive integers. Find the consecutive sums giving the
polite numbers 544 and 424. What characterizes impolite numbers?