Arithmetic sequences

problem
Favourite

Charlie's Delightful Machine

Age

11 to 16

Challenge level

1 out of 3

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
problem
Favourite

A Little Light Thinking

Age

14 to 16

Challenge level

1 out of 3

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
problem
Favourite

Steel Cables

Age

14 to 16

Challenge level

1 out of 3

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
problem
Favourite

Mystic Rose

Age

14 to 16

Challenge level

2 out of 3

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem
Favourite

Prime AP

Age

16 to 18

Challenge level

1 out of 3

What can you say about the common difference of an AP where every term is prime?
problem

Matchsticks

Age

7 to 11

Challenge level

1 out of 3

Reasoning about the number of matches needed to build squares that share their sides.
problem

Transformations Tables

Age

7 to 11

Challenge level

1 out of 3

These grids are filled according to some rules - can you complete them?
problem

Squares, Squares and More Squares

Age

11 to 14

Challenge level

1 out of 3

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
problem

Janusz Asked

Age

16 to 18

Challenge level

2 out of 3

In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?
problem

Skip Counting

Age

5 to 7

Challenge level

1 out of 3

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.