Describing patterns and sequences

problem
Farey sequences

Age

11 to 14

Challenge level

There are lots of ideas to explore in these sequences of ordered fractions.
problem
Lastly - well

Age

11 to 14

Challenge level

What are the last two digits of 2^(2^2003)?
problem
Beads

Age

7 to 11

Challenge level

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
problem
Even up

Age

11 to 14

Challenge level

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?
problem
Sept03 Sept03 Sept03

Age

7 to 11

Challenge level

This number has 903 digits. What is the sum of all 903 digits?
problem
Sept 03

Age

11 to 14

Challenge level

What is the last digit of the number 1 / 5^903 ?
problem
Frogs

Age

11 to 14

Challenge level

How many moves does it take to swap over some red and blue frogs? Do you have a method?
problem
Sets of numbers

Age

7 to 11

Challenge level

How many different sets of numbers with at least four members can you find in the numbers in this box?
problem
The mathemagician's seven spells

Age

7 to 11

Challenge level

"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?
problem
Transformation tease

Age

7 to 11

Challenge level

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?