Problems
Change Around
Stage:1 Challenge Level:
Move just three of the circles so that the triangle faces in the opposite direction.
Number Round Up
Stage:1 Challenge Level:
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Round and Round the Circle
Stage:2 Challenge Level:
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Watching the Wheels Go 'round and 'round
Stage:2 Challenge Level:
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Red Balloons, Blue Balloons
Stage:2 Challenge Level:
Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?
Spelling Circle
Stage:2 Challenge Level:
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
Borromean Mind Boggler
Stage:2 Challenge Level:
What colours of circles do you think link with each other? If you remove one ring what will happen to the other two?
World of Tan - Time Flies
Stage:2 Challenge Level:
Can you fit the tangram pieces into the outlines of the candle and sundial?
Magic 14
Stage:2 Challenge Level:
Place the numbers from 1 to 14 inclusive in the empty circles to make a total of 30 along each line of four circles.
Family Tree
Stage:2 Challenge Level:
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Redblue
Stage:2 Challenge Level:
Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
Cayley
Stage:3 Challenge Level:
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Screwed-up
Stage:3 Challenge Level:
A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?
One to Eight
Stage:3 Challenge Level:
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
Platonic Planet
Stage:4 Challenge Level:
Az'glqssk the alien lives on a platonic planet whose shape is that of a perfect regular dodecahedron. Being extremely xenophobic, she checks every day that no-one else has arrived on her planet. In. . . .
Cosines Rule
Stage:4 Challenge Level:
Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove that AP^2/AB.AC + CP^2/CA.CB = 1 + PB^2/BA.BC
Six Circles
Stage:4 Challenge Level:
Six circles, all of radius 1 unit, are packed in 4 different shaped boxes so that the circles touch their neighbours and the sides of the box. Without using any calculations, compare the areas of the. . . .
Around and Back
Stage:4 Challenge Level:
A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .
Binomial
Stage:5 Challenge Level:
By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn
