Conjecturing and generalising

problem
Maxagon

Age

11 to 14

Challenge level

What's the greatest number of sides a polygon on a dotty grid could have?
problem
Regular hexagon loops

Age

11 to 14

Challenge level

Make some loops out of regular hexagons. What rules can you discover?
problem
Last-but-one

Age

14 to 16

Challenge level

What is the last-but-one digit of 99! ?
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...
problem
Multiple surprises

Age

11 to 16

Challenge level

Sequences of multiples keep cropping up...
problem
Fibonacci surprises

Age

11 to 14

Challenge level

Play around with the Fibonacci sequence and discover some surprising results!
problem
Six ten total

Age

7 to 11

Challenge level

This challenge combines addition, multiplication, perseverance and even proof.
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
Beach huts

Age

11 to 14

Challenge level

Can you figure out how sequences of beach huts are generated?