Powers and roots

problem
Roots near 9

Age

14 to 16

Challenge level

For how many integers ð‘› is the difference between âˆšð‘› and 9 is less than 1?
problem
Double trouble

Age

14 to 16

Challenge level

Simple additions can lead to intriguing results...
problem
Function pyramids

Age

16 to 18

Challenge level

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
problem
Googol

Age

16 to 18

Challenge level

Find the smallest value for which a particular sequence is greater than a googol.
problem
Irrational arithmagons

Age

16 to 18

Challenge level

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?
problem
Fit for photocopying

Age

14 to 16

Challenge level

Explore the relationships between different paper sizes.
problem
Archimedes numerical roots

Age

16 to 18

Challenge level

How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
problem
Powerful order

Age

14 to 16

Challenge level

Powers of numbers might look large, but which of these is the largest...
problem
Near 10

Age

14 to 16

Challenge level

10 must remain within easy reach...
problem
Age of augustus

Age

11 to 14

Challenge level

The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?