Comparing and ordering numbers

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

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.

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.

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

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?

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.

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

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

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?

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?