Being curious

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?

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

There are many different methods to solve this geometrical problem - how many can you find?

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

Which set of numbers that add to 100 have the largest product?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

There are lots of different methods to find out what the shapes are worth - how many can you find?

How many winning lines can you make in a three-dimensional version of noughts and crosses?