# Patterns and Sequences Short Problems

### Weekly Problem 17 - 2011

##### Stage: 2 and 3 Short Challenge Level:

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

### Weekly Problem 23 - 2011

##### Stage: 2 and 3 Short Challenge Level:

MatildaMatildaMatil... What is the 1000th letter?

### Weekly Problem 36 - 2010

##### Stage: 2 and 3 Short Challenge Level:

How many squares are needed to continue this pattern?

### Weekly Problem 38 - 2009

##### Stage: 3 Short Challenge Level:

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

### Weekly Problem 35 - 2010

##### Stage: 3 Short Challenge Level:

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

### Weekly Problem 42 - 2012

##### Stage: 3 Challenge Level:

Weekly Problem 42 - 2012

### Weekly Problem 3 - 2008

##### Stage: 3 and 4 Challenge Level:

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

### Weekly Problem 35 - 2014

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 35 - 2014

### Weekly Problem 45 - 2015

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 45 - 2015

### Weekly Problem 20 - 2008

##### Stage: 3 and 4 Challenge Level:

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?

### Weekly Problem 8 - 2015

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 8 - 2015

### Weekly Problem 47 - 2015

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 47 - 2015

### Weekly Problem 11 - 2015

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 11 - 2015

### Weekly Problem 13 - 2015

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 13 - 2015

### Weekly Problem 29 - 2015

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 29 - 2015

### Weekly Problem 52 - 2010

##### Stage: 3 and 4 Short Challenge Level:

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

### Weekly Problem 8 - 2011

##### Stage: 3 and 4 Short Challenge Level:

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

### Weekly Problem 6 - 2014

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 6 - 2014

### Weekly Problem 39 - 2015

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 39 - 2015

### Weekly Problem 9 - 2011

##### Stage: 3 and 4 Short Challenge Level:

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?

### Weekly Problem 8 - 2014

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 8 - 2014

### Weekly Problem 44 - 2015

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 44 - 2015

### Weekly Problem 41 - 2012

##### Stage: 4 Challenge Level:

Weekly Problem 41 - 2012

### Weekly Problem 44 - 2012

##### Stage: 4 Challenge Level:

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

### Weekly Problem 46 - 2012

##### Stage: 4 Challenge Level:

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?

### Weekly Problem 34 - 2015

##### Stage: 4 Challenge Level:

Weekly Problem 34 - 2015