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

Count Back

KS 3 Short Challenge Level:

 Challenge Level:1

How well can you count back from sixty thousand?

Negative Dice

KS 3 Short Challenge Level:

 Challenge Level:1

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

Debt Recovery

KS 3 Short Challenge Level:

 Challenge Level:1

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

Tick Tock

KS 3 Short Challenge Level:

 Challenge Level:1

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

Loose Change

KS 3 Short Challenge Level:

 Challenge Level:1

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

Paying the Bill

KS 3 Short Challenge Level:

 Challenge Level:1

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

Mathematical Ages

KS 3 Short Challenge Level:

 Challenge Level:1

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

Quiz Questions

KS 3 Short Challenge Level:

 Challenge Level:1

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

Mini Kakuro

KS 3 Short Challenge Level:

 Challenge Level:1

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:

 Challenge Level:1

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

Highs and Lows

KS 3 Short Challenge Level:

 Challenge Level:1

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

Central Sum

KS 3 Short Challenge Level:

 Challenge Level:1

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

KS 3 Short Challenge Level:

 Challenge Level:1

Can you solve this magic square?

Alberta's Age

KS 3 Short Challenge Level:

 Challenge Level:2 Challenge Level:2

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

Double with 1 to 9

KS 3 Short Challenge Level:

 Challenge Level:2 Challenge Level:2

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

Sum Up

KS 3 Short Challenge Level:

 Challenge Level:2 Challenge Level:2

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

Missing 9s

KS 3 Short Challenge Level:

 Challenge Level:2 Challenge Level:2

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

Itchy's Fleas

KS 3 Short Challenge Level:

 Challenge Level:2 Challenge Level:2

Itchy the dog has a million fleas. How many fleas might his shampoo kill?

Even Squares

KS 3 Short Challenge Level:

 Challenge Level:2 Challenge Level:2

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

Digit Sum Puzzle

KS 3 Short Challenge Level:

 Challenge Level:3 Challenge Level:3 Challenge Level:3

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

KS 3 Short Challenge Level:

 Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Equal Length Powers

KS 4 Short Challenge Level:

 Challenge Level:1

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

Pros and Cons

KS 4 Short Challenge Level:

 Challenge Level:2 Challenge Level:2

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

How Many Digits?

KS 4 Short Challenge Level:

 Challenge Level:2 Challenge Level:2

How many digits are there in this product?

Number Crunch

KS 4 Short Challenge Level:

 Challenge Level:3 Challenge Level:3 Challenge Level:3

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

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2018. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.