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It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Which set of numbers that add to 100 have the largest product?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
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?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Can you work out how to produce different shades of pink paint?
Take a look at the video and try to find a sequence of moves that will untangle the ropes.
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Can you make sense of information about trees in order to maximise the profits of a forestry company?