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.

problem

Expanding pattern

Age

11 to 14

Challenge level

How many squares are needed to continue this pattern?

problem

Fibonacci deduction

Age

11 to 14

Challenge level

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

problem

Fruit line-up

Age

11 to 14

Challenge level

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

problem

Printing error

Age

11 to 14

Challenge level

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

problem

Many Matildas

Age

11 to 14

Challenge level

MatildaMatildaMatil... What is the 1000th letter?

problem

What a coincidence!

Age

11 to 14

Challenge level

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

problem

Suit sequence

Age

11 to 14

Challenge level

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

problem

Street lamps

Age

11 to 14

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?

problem

Triangular clock

Age

11 to 14

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?

problem

Pattern snake

Age

11 to 14

Challenge level

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

problem

Hexagon line

Age

11 to 14

Challenge level

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

problem

Sliding robot

Age

11 to 14

Challenge level

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

problem

How many rectangles?

Age

11 to 14

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?

problem

Knockdown

Age

11 to 14

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?

problem

Square grid

Age

11 to 14

Challenge level

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

problem

Tiled floor

Age

11 to 14

Challenge level

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

problem

Night watchmen

Age

11 to 14

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?

problem

Knights and knaves

Age

11 to 14

Challenge level

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

problem

Doubly consecutive sums

Age

11 to 14

Challenge level

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

problem

Even up

Age

11 to 14

Challenge 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?