Explaining, convincing and proving

game

The triangle game

Age

11 to 16

Challenge level

Can you discover whether this is a fair game?
game

Online

Age

7 to 11

Challenge level

Can you end up with all the occurrences of the same letter in this two-player game?
game

Yih or Luk tsut k'i or Three Men's Morris

Age

11 to 18

Challenge level

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.
problem
Anti-magic square

Age

11 to 14

Challenge level

You may have met Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different - can you still solve it?
problem
Exponential intersection

Age

16 to 18

Challenge level

Can the pdfs and cdfs of an exponential distribution intersect?
problem
Next-door numbers

Age

5 to 7

Challenge level

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
problem
Angles inside

Age

11 to 14

Challenge level

Draw some angles inside a rectangle. What do you notice? Can you prove it?
problem
Number lines in disguise

Age

7 to 14

Challenge level

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
problem
More number sandwiches

Age

11 to 16

Challenge level

When is it impossible to make number sandwiches?
problem
Robotic rotations

Age

11 to 16

Challenge level

How did the the rotation robot make these patterns?