This is part of our collection of Short Problems.
You may also be interested in our longer problems on Place Value, Integers, Ordering and Rounding.
Printable worksheets containing selections of these problems are available here.
problem
Debt recovery
Age
11 to 14
Challenge level
Tony and Tina can't work out which of them owes what to the other. Can you?
problem
Loose change
Age
11 to 14
Challenge level
In how many ways can you give change for a ten pence piece?
problem
Mathematical ages
Age
11 to 14
Challenge level
Arrange these three famous mathematicians in order with the shortest-lived first.
problem
Quiz questions
Age
11 to 14
Challenge level
Jack does a 20-question quiz. How many questions didn't he attempt?
problem
Highs and lows
Age
11 to 14
Challenge level
What were the maximum and minimum temperatures recorded in my max/min thermometer?
problem
Reverse ages
Age
11 to 14
Challenge level
When is the next time that Brian's age will be the reverse of his father's age?
problem
Rough rectangle
Age
11 to 14
Challenge level
What is the smallest possible area that this rectangle could have?
problem
Central sum
Age
11 to 14
Challenge level
Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?
problem
Negative dice
Age
11 to 14
Challenge level
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?
problem
Mini Kakuro
Age
11 to 14
Challenge level
The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?
problem
Even squares
Age
11 to 14
Challenge level
Can you find squares within a number grid whose entries add up to an even total?
problem
Double with 1 to 9
Age
11 to 14
Challenge level
Can you find a number and its double using the digits $1$ to $9$ only once each?
problem
Digital book
Age
11 to 14
Challenge level
If it takes 852 digits to number all the pages of a book, what is the number of the last page?
problem
Missing 9s
Age
11 to 14
Challenge level
Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?
problem
Tick tock
Age
11 to 14
Challenge level
Tick's watch is slow and Tock's watch is fast. How long is it before their watches differ by an hour?
problem
Paying the bill
Age
11 to 14
Challenge level
Gill and I went out to lunch. We agreed to split the total cost equally. How much did I owe Gill?
problem
Digit sum puzzle
Age
11 to 14
Challenge level
Let N be the smallest positive integer whose digits add up to 2015. What is the sum of the digits of N+1?
problem
Equal length powers
Age
14 to 16
Challenge level
How many positive integers $n$ exist for which $n^2$ has the same number of digits as $n^3$?
problem
Alberta's age
Age
14 to 16
Challenge level
Alberta won't reveal her age. Can you work it out from these clues?
problem
Repeat product
Age
14 to 16
Challenge level
Can you work out the value of P+Q+R in the multiplication shown?
problem
Sum up
Age
14 to 16
Challenge level
David listed ten consecutive numbers and removed one of them. Which number did he remove?
problem
Pros and cons
Age
14 to 16
Challenge level
If p is a positive integer and q is a negative integer, which of these expressions is the greatest?
problem
Digital counter
Age
14 to 16
Challenge level
When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?
problem
Number crunch
Age
14 to 16
Challenge level
Create 24 numbers from four digits. Why is 101 always a factor of their sum?
problem
How many gorillas?
Age
14 to 16
Challenge level
If the numbers in this news article have been estimated, then what is the largest number of gorillas that there could have been 10 years ago?
problem
Digit sum
Age
14 to 16
Challenge level
What is the sum of all the digits in all the integers from one to one million?