Comparing and ordering numbers

problem
Favourite

Consecutive Seven

Age

11 to 14

Challenge level

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?
problem
Favourite

Farey Sequences

Age

11 to 14

Challenge level

There are lots of ideas to explore in these sequences of ordered fractions.
problem
Favourite

Difference Sudoku

Age

14 to 16

Challenge level

Use the differences to find the solution to this Sudoku.
problem
Favourite

Giants

Age

16 to 18

Challenge level

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?
problem

Greetings

Age

11 to 14

Challenge level

From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How many such students are there?
problem

Fractions Made Faster

Age

7 to 11

Challenge level

Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!
problem

Move a Match

Age

7 to 11

Challenge level

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
problem

Pros and Cons

Age

14 to 16

Challenge level

If p is a positive integer and q is a negative integer, which of these expressions is the greatest?
problem

Rachel's Problem

Age

14 to 16

Challenge level

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
problem

17s and 23s

Age

11 to 14

Challenge level

Can you form this 2010-digit number...