Exploring and noticing

problem
Magic crosses

Age

7 to 14

Challenge level

Can you find examples of magic crosses? Can you find all the possibilities?
problem
Polygon rings

Age

11 to 14

Challenge level

Join pentagons together edge to edge. Will they form a ring?
problem
Where are you flying?

Age

14 to 18

Challenge level

Where do people fly to from London? What is good and bad about these representations?
problem
Bundles of cubes

Age

7 to 11

Challenge level

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
problem
Oldest and youngest

Age

14 to 16

Challenge level

Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?
problem
Suit sequence

Age

11 to 14

Challenge level

A pattern repeats every six symbols. What are the 100th and 101st symbols?
problem
Knockdown

Age

11 to 14

Challenge level

Weekly Problem 51 - 2016
Pegs numbered 1 to 50 are placed in a row. Alternate pegs are knocked down, and this process is repeated. What is the number of the last peg to be knocked down?
problem
How many rectangles?

Age

11 to 14

Challenge level

By drawing 5 horizontal and four vertical lines, one can form 12 rectangles. What is the greatest number of rectangles that can be formed by drawing 15 lines?
problem
Growing surprises

Age

11 to 14

Challenge level

Can you find the connections between linear and quadratic patterns?
problem
Square number surprises

Age

14 to 16

Challenge level

There are unexpected discoveries to be made about square numbers...