# Patterns and Sequences Stage 3 - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Patterns and Sequences - Stage 3.

Printable worksheets containing selections of these problems are available here:

 Stage 3 ★ Sheet 1 Solutions Sheet 2 Solutions

### Street Lamps

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 9 - 2007
Walking up a steep hill, I pass 10 equally spaced street lamps. How long do I take to walk from the first lamp to the last?

### Printing Error

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 17 - 2011
Every third page number in this book has been omitted. Can you work out what number will be on the last page?

### Many Matildas

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 23 - 2011
MatildaMatildaMatil... What is the 1000th letter?

### Starting Fibonacci

##### KS 3 Short Challenge Level:

Weekly Problem 40 - 2012
What is the first term of a Fibonacci sequence whose second term is 4 and fifth term is 22?

### 12345

##### KS 3 Short Challenge Level:

Weekly Problem 50 - 2011
Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?

### Hexagon Line

##### KS 3 Short Challenge Level:

Weekly Problem 5 - 2016
How many hexagons are required for the perimeter of the whole shape to have length 1002cm?

### Expanding Pattern

##### KS 3 Short Challenge Level:

Weekly Problem 36 - 2010
How many squares are needed to continue this pattern?

### Luis' Seven

##### KS 3 Short Challenge Level:

Weekly Problem 6 - 2016
Luis writes down seven consecutive positive integers. The sum of the three smallest numbers is 33. What is the sum of the three largest numbers?

### Triangular Clock

##### KS 3 Short Challenge Level:

Weekly Problem 31 - 2007
Trinni rearanges numbers on a clock face so each adjacent pair add up to a triangle number... What number did she put where 6 would usually be?

### Triangle of Squares

##### KS 3 Short Challenge Level:

Weekly Problem 42 - 2012
What number appears immediately below 400 in the triangle?

### Pattern Snake

##### KS 3 Short Challenge Level:

Weekly Problem 27 - 2010
This pattern repeats every 12 dots. Can you work out what a later piece will be?

### Trolley Park

##### KS 3 Short Challenge Level:

Weekly Problem 14 - 2016
In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?

### Knights and Knaves

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 35 - 2010
Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?

### Fruit Line-up

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 8 - 2011
This grocer wants to arrange his fruit in a particular order, can you help him?

### Powerful Finale

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 24 - 2017
What is the last digit of $3^{2011}$?

### Night Watchmen

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 20 - 2008
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?

### Doubly Consecutive Sums

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 51 - 2017
How many numbers less than 2017 are both the sum of two consecutive integers and the sum of five consecutive integers?

### Collatz-ish

##### KS 4 Short Challenge Level:

Weekly Problem 35 - 2014
A sequence is generated using these rules. For which values of n is the nth term equal to n?

### Alternating Sum

##### KS 4 Short Challenge Level:

Weekly Problem 1 - 2008
Given that the number 2008 is the correct answer to a sum, can you find n?