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:

 Stage 3 ★ Sheet 1 Solutions Sheet 2 Solutions Sheet 3 Solutions

Alberta's Age

KS 3 Short Challenge Level:

Weekly Problem 26 - 2011
Alberta won't reveal her age. Can you work it out from these clues?

Debt Recovery

KS 3 Short Challenge Level:

Weekly Problem 7 - 2009
Tony and Tina can't work out which of them owes what to the other. Can you?

Sum One Special

KS 3 Short Challenge Level:

Weekly Problem 1 - 2007
Three integers have a sum of 1 and a product of 36 - what are they?

Double with 1-9

KS 3 Short Challenge Level:

Weekly Problem 31 - 2011
Can you find a number and its double using the digits $1$ to $9$ only once each?

Loose Change

KS 3 Short Challenge Level:

Weekly Problem 10 - 2009
In how many ways can you give change for a ten pence piece?

Paying the Bill

KS 3 Short Challenge Level:

Weekly Problem 44 - 2007
Gill and I went to a restaurant for lunch to celebrate her birthday....We agreed to split the total cost equally. How much did I owe Gill?

Mathematical Ages

KS 3 Short Challenge Level:

Weekly Problem 16 - 2009
Arrange these three famous mathematicians in order with the shortest-lived first.

Pros and Cons

KS 3 Short Challenge Level:

Weekly Problem 17 - 2008
If p is a positive integer and q is a negative integer, which of these expressions is the greatest?

Itchy's Fleas

KS 3 Short Challenge Level:

Weekly Problem 32 - 2017
Itchy has a million fleas. His anti-flea leaves no more than 1% of the original fleas after use. What is the least number of fleas that the shampoo will remove?

Central Sum

KS 3 Short Challenge Level:

Weekly Problem 53 - 2011
Find a number between 100 and 999 that has its middle digit equal to the sum of the other two digits. Can you find all possibilities?

Quiz Questions

KS 3 Short Challenge Level:

Weekly Problem 25 - 2009
Jack does a 20-question quiz. How many questions didn't he attempt?

Mini Kakuro

KS 3 Short Challenge Level:

Weekly Problem 21 - 2008
The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?

Reverse Ages

KS 3 Short Challenge Level:

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

Negative Dice

KS 3 Short Challenge Level:

Weekly Problem 16 - 2012
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

Highs and Lows

KS 3 Short Challenge Level:

Weekly Problem 32 - 2009
I have a max/min thermometer in my greenhouse. What were the maximum and minimum temperatures recorded when I looked at it on Wednesday evening?

Even Squares

KS 3 Short Challenge Level:

Weekly Problem 27 - 2008
Can you find squares within a number grid whose entries add up to an even total?

Tick Tock

KS 3 Short Challenge Level:

Weekly Problem 10 - 2006
Tick's watch is slow and Tock's watch is fast. How long is it before their watches differ by an hour?

Different Magic Square

KS 3 Short Challenge Level:

Weekly Problem 47 - 2008
Can you solve this magic square?

Count Back

KS 3 Short Challenge Level:

How well can you count back from sixty thousand?

Cibara Numerals

KS 3 Short Challenge Level:

Weekly problem 47 - 2006
Cibara numerals are the same shape as Arabic numerals, but are used in the opposite order. Working in Cibara numerals, what is the answer to 837 + 742?

Sum Up

KS 3 Short Challenge Level:

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

Missing 9s

KS 3 Short Challenge Level:

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

Digit Sum Puzzle

KS 3 Short 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?

Equal Length Powers

KS 4 Short Challenge Level:

Weekly Problem 33 - 2010
How many positive integers $n$ exist for which $n^2$ has the same number of digits as $n^3$?

How Many Digits?

KS 4 Short Challenge Level:

How many digits are there in this product?

Repeat Product

KS 4 Short Challenge Level:

Weekly Problem 3 - 2014
Can you work out the value of P+Q+R in the multiplication shown?

Number Crunch

KS 4 Short Challenge Level:

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