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!

Age 11 to 14 Short Challenge Level:

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

Expanding Pattern

Age 11 to 14 Short Challenge Level:

How many squares are needed to continue this pattern?

Street Lamps

Age 11 to 14 Short Challenge 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?

Fibonacci Deduction

Age 11 to 14 Short Challenge Level:

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

Suit Sequence

Age 11 to 14 Short Challenge Level:

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

Triangular Clock

Age 11 to 14 Short Challenge 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?

Fruit Line-up

Age 11 to 14 Short Challenge Level:

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

Printing Error

Age 11 to 14 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?

Many Matildas

Age 11 to 14 Short Challenge Level:

MatildaMatildaMatil... What is the 1000th letter?

Square Grid

Age 11 to 14 Short Challenge Level:

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

How Many Rectangles?

Age 11 to 14 Short Challenge 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?

Tiled Floor

Age 11 to 14 Short Challenge Level:

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

Knockdown

Age 11 to 14 Short Challenge 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?

Hexagon Line

Age 11 to 14 Short Challenge Level:

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

Night Watchmen

Age 11 to 14 Short 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?

Pattern Snake

Age 11 to 14 Short Challenge Level:

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

Sliding Robot

Age 11 to 14 Short Challenge Level:

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

Knights and Knaves

Age 11 to 14 Short Challenge Level:

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

Doubly Consecutive Sums

Age 11 to 14 Short Challenge Level:

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

Below 400

Age 14 to 16 Short Challenge Level:

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

Collatz 13

Age 14 to 16 Short 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?

Collatz-ish

Age 14 to 16 Short Challenge Level:

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

Alternating Sum

Age 14 to 16 Short Challenge Level:

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

Diagonals

Age 14 to 16 Short Challenge Level:

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

Trolley Park

Age 14 to 16 Short Challenge Level:

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

Difference Sequence

Age 14 to 16 Short Challenge Level:

When will 2000 appear in this sequence?

12345

Age 14 to 16 Short Challenge Level:

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

Newspaper Sheets

Age 14 to 16 Short Challenge Level:

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