Year 11 Being curious

problem
How old am I?

Age

14 to 16

Challenge level

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
problem
Beelines

Age

14 to 16

Challenge level

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
problem
Triangle midpoints

Age

14 to 16

Challenge level

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
problem
Triangles and petals

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?
problem
Partly painted cube

Age

14 to 16

Challenge level

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
problem
Same number!

Age

14 to 16

Challenge level

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
problem
Multiplication arithmagons

Age

14 to 16

Challenge level

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
problem
Odds and evens made fair

Age

14 to 16

Challenge level

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.
problem
Fit for photocopying

Age

14 to 16

Challenge level

Explore the relationships between different paper sizes.