Comparing and ordering numbers

problem
A numbered route

Age

7 to 11

Challenge level

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
problem
Farey sequences

Age

11 to 14

Challenge level

There are lots of ideas to explore in these sequences of ordered fractions.
problem
The magic number and the hepta-tree

Age

7 to 11

Challenge level

Find the exact difference between the largest ball and the smallest ball on the Hepta Tree and then use this to work out the MAGIC NUMBER!
problem
Highest and lowest

Age

7 to 11

Challenge level

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
problem
Largest number

Age

11 to 14

Challenge level

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
problem
Mathland election

Age

11 to 14

Challenge level

A political commentator summed up an election result. Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.
problem
Which scripts?

Age

7 to 11

Challenge level

There are six numbers written in five different scripts. Can you sort out which is which?
problem
Euromaths

Age

11 to 14

Challenge level

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?
problem
Writ large

Age

11 to 14

Challenge level

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.
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!