On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
What is the greatest number of squares you can make by overlapping three squares?
Ben has five coins in his pocket. How much money might he have?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?
Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.
In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation. . . .