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# Patterns and Sequences - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Patterns and Sequences Age 11-14 and Age 14-16.

Printable worksheets containing selections of these problems are available here.

### What a Coincidence!

### Expanding Pattern

### Street Lamps

### Fibonacci Deduction

### Suit Sequence

### Triangular Clock

### Fruit Line-up

### Printing Error

### How Many Rectangles?

### Tiled Floor

### Knockdown

### Hexagon Line

### Night Watchmen

### Pattern Snake

### Sliding Robot

### Square Grid

### Doubly Consecutive Sums

### Even Up

### Knights and Knaves

### Below 400

### Collatz 13

### Collatz-ish

### Alternating Sum

### Diagonals

### Trolley Park

### 12345

### Newspaper Sheets

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This is part of our collection of Short Problems.

You may also be interested in our longer problems on Patterns and Sequences Age 11-14 and Age 14-16.

Printable worksheets containing selections of these problems are available here.

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

How many squares are needed to continue this pattern?

Age 11 to 14

ShortChallenge Level

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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

A pattern repeats every six symbols. What are the 100th and 101st symbols?

Age 11 to 14

ShortChallenge Level

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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

By drawing 5 horizontal and four vertical lines, one can form 12 rectangles. What is the greatest number of rectangles that can be formed by drawing 15 lines?

Age 11 to 14

ShortChallenge Level

This tiled floor has 109 purple tiles. How many tiles are there altogether?

Age 11 to 14

ShortChallenge Level

Weekly Problem 51 - 2016

Pegs numbered 1 to 50 are placed in a row. Alternate pegs are knocked down, and this process is repeated. What is the number of the last peg to be knocked down?

Age 11 to 14

ShortChallenge Level

How many hexagons are required for the perimeter of the whole shape to have length 1002cm?

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

This pattern repeats every 12 dots. Can you work out what a later piece will be?

Age 11 to 14

ShortChallenge Level

A robot moves along the number line. Where will it be after 2011 slides?

Age 11 to 14

ShortChallenge Level

Can you work out what fraction of this grid is shaded?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

Age 11 to 14

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

Can you work out which number will appear directly below 400 in this pattern?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

A sequence is generated using these rules. For which values of n is the nth term equal to n?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

How many diagonals does a regular icosagon (20 sides) have?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?

Age 14 to 16

ShortChallenge Level

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?