List

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.

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
problem

Triangular Clock

Age
11 to 14
Challenge level

Trinni rearranges 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?

Small pepper seedlings in orange pots.
problem

Expanding Pattern

Age
11 to 14
Challenge level

How many squares are needed to continue this pattern?

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
problem

Many Matildas

Age
11 to 14
Challenge level

MatildaMatildaMatil... What is the 1000th letter?

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
problem

Suit Sequence

Age
11 to 14
Challenge level

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

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
problem

Sliding Robot

Age
11 to 14
Challenge level

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

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
problem

Square Grid

Age
11 to 14
Challenge level

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

Small pepper seedlings in orange pots.
problem

Tiled Floor

Age
11 to 14
Challenge level

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

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
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?

Small pepper seedlings in orange pots.
problem

Collatz-Ish

Age
14 to 16
Challenge level

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

Small pepper seedlings in orange pots.
problem

Trolley Park

Age
14 to 16
Challenge level

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

Small pepper seedlings in orange pots.
problem

Diagonals

Age
14 to 16
Challenge level

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

Small pepper seedlings in orange pots.
problem

Difference Sequence

Age
14 to 16
Challenge level

When will 2000 appear in this sequence?

Small pepper seedlings in orange pots.
problem

12345

Age
14 to 16
Challenge level

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

Small pepper seedlings in orange pots.
problem

Below 400

Age
14 to 16
Challenge level

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

Small pepper seedlings in orange pots.
problem

Alternating Sum

Age
14 to 16
Challenge level

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

Small pepper seedlings in orange pots.
problem

Newspaper Sheets

Age
14 to 16
Challenge level

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

Small pepper seedlings in orange pots.
problem

Collatz 13

Age
14 to 16
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?