Every third page number in this book has been omitted. Can you work out what number will be on the last page?

MatildaMatildaMatil... What is the 1000th letter?

How many squares are needed to continue this pattern?

This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?

Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?

Counters are placed on an 8 by 8 chessboard... What fraction of the counters are on squares of the same colour as themselves?

Grannie's watch gains 30 minutes every hour, whilst Grandpa's watch loses 30 minutes every hour. What is the correct time when their watches next agree?

Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?

This grocer wants to arrange his fruit in a particular order, can you help him?

Barbara is putting draughts on a $4x4$ board in a particular way. Can you find the least number of draughts she needs to put down?

Consider two arithmetic sequences: 1998, 2005, 2012,... and 1996, 2005, 2014,... Which numbers will appear in both?

If a number is even, halve it; if odd, treble it and add 1. If a sequence starts at 13, what will be the value of the 2008th term?