Place Value, Integers, Ordering and Rounding - Short Problems

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.

Debt Recovery

Age 11 to 14 ShortChallenge Level

Tony and Tina can't work out which of them owes what to the other. Can you?

Count Back

Age 11 to 14 ShortChallenge Level

How well can you count back from sixty thousand?

Loose Change

Age 11 to 14 ShortChallenge Level

In how many ways can you give change for a ten pence piece?

Mathematical Ages

Age 11 to 14 ShortChallenge Level

Arrange these three famous mathematicians in order with the shortest-lived first.

Quiz Questions

Age 11 to 14 ShortChallenge Level

Jack does a 20-question quiz. How many questions didn't he attempt?

Mini Kakuro

Age 11 to 14 ShortChallenge Level

The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?

Highs and Lows

Age 11 to 14 ShortChallenge Level

What were the maximum and minimum temperatures recorded in my max/min thermometer?

Reverse Ages

Age 11 to 14 ShortChallenge Level

When is the next time that Brian's age will be the reverse of his father's age?

Central Sum

Age 11 to 14 ShortChallenge Level

Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?

Different Magic Square

Age 11 to 14 ShortChallenge Level

Can you solve this magic square?

Negative Dice

Age 11 to 14 ShortChallenge Level

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

Rough Rectangle

Age 11 to 14 ShortChallenge Level

What is the smallest possible area that this rectangle could have?

Tick Tock

Age 11 to 14 ShortChallenge Level

Tick's watch is slow and Tock's watch is fast. How long is it before their watches differ by an hour?

Double with 1 to 9

Age 11 to 14 ShortChallenge Level

Can you find a number and its double using the digits $1$ to $9$ only once each?

Paying the Bill

Age 11 to 14 ShortChallenge Level

Gill and I went out to lunch. We agreed to split the total cost equally. How much did I owe Gill?

Digital Book

Age 11 to 14 ShortChallenge Level

If it takes 852 digits to number all the pages of a book, what is the number of the last page?

Missing 9s

Age 11 to 14 ShortChallenge Level

Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?

Even Squares

Age 11 to 14 ShortChallenge Level

Can you find squares within a number grid whose entries add up to an even total?

Digit Sum Puzzle

Age 11 to 14 ShortChallenge Level

Let N be the smallest positive integer whose digits add up to 2015. What is the sum of the digits of N+1?

Repeat Product

Age 14 to 16 ShortChallenge Level

Can you work out the value of P+Q+R in the multiplication shown?

Sum Up

Age 14 to 16 ShortChallenge Level

David listed ten consecutive numbers and removed one of them. Which number did he remove?

Pros and Cons

Age 14 to 16 ShortChallenge Level

If p is a positive integer and q is a negative integer, which of these expressions is the greatest?

How Many Digits?

Age 14 to 16 ShortChallenge Level

How many digits are there in this product?

Equal Length Powers

Age 14 to 16 ShortChallenge Level

How many positive integers $n$ exist for which $n^2$ has the same number of digits as $n^3$?

Alberta's Age

Age 14 to 16 ShortChallenge Level

Alberta won't reveal her age. Can you work it out from these clues?

Digital Counter

Age 14 to 16 ShortChallenge Level

When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?

Digit Sum

Age 14 to 16 ShortChallenge Level

What is the sum of all the digits in all the integers from one to one million?

How Many Gorillas?

Age 14 to 16 ShortChallenge 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?

Number Crunch

Age 14 to 16 ShortChallenge Level

Create 24 numbers from four digits. Why is 101 always a factor of their sum?