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
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
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
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
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?
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
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?
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
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?
problem
Below 400
Age
14 to 16
Challenge level
Can you work out which number will appear directly below 400 in this pattern?
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?
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?
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?
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?
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?
problem
Diagonals
Age
14 to 16
Challenge level
How many diagonals does a regular icosagon (20 sides) have?