Being curious

A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Can you find a way to identify times tables after they have been shifted up or down?

Invent a scoring system for a 'guess the weight' competition.

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Can you find rectangles where the value of the area is the same as the value of the perimeter?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

I'm thinking of a rectangle with an area of 24. What could its perimeter be?