There are 25 NRICH Mathematical resources connected to Number bases, you may find related items under Place value and the number system.
Broad Topics > Place value and the number system > Number bases
Guesswork
Age 14 to 16
Challenge Level
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
Oh for the Mathematics of Yesteryear
Age 11 to 14
Challenge Level
A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45 days against the siege of the enemy?
Secret Transmissions
Age 14 to 16
Challenge Level
How can Agent X transmit data on a faulty line and be sure that her message will get through?
More Secret Transmissions
Age 16 to 18
Challenge Level
In 'Secret Transmissions', Agent X could send four-digit codes error free. Can you devise an error-correcting system for codes with more than four digits?
Fingers and Hands
Age 7 to 11
Challenge Level
How would you count the number of fingers in these pictures?
Balance Power
Age 11 to 18
Challenge Level
Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?
Alien Counting
Age 7 to 11
Challenge Level
Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.
A Story about Absolutely Nothing
Age 7 to 18
This article for the young and old talks about the origins of our number system and the important role zero has to play in it.
The Knapsack Problem and Public Key Cryptography
Age 16 to 18
An example of a simple Public Key code, called the Knapsack Code is described in this article, alongside some information on its origins. A knowledge of modular arithmetic is useful.
Knapsack
Age 14 to 16
Challenge Level
You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.
Composite Notions
Age 14 to 16
Challenge Level
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
Phew I'm Factored
Age 14 to 16
Challenge Level
Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.
Learn about Number Bases
Age 11 to 18
We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.
Back to the Planet of Vuvv
Age 11 to 14
Challenge Level
There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of the creatures they could see. The creature looking to the West wrote 122. The creature looking to the East wrote 22. The creature looking to the South wrote 101. The creature looking to the North wrote 41. In which direction are the 2 Zios looking and in which directions are the 2 Zepts looking?
Basically
Age 11 to 14
Challenge Level
The number 3723(in base 10) is written as 123 in another base. What is that base?
Happy Octopus
Age 11 to 14
Challenge Level
This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 ... Find all the fixed points and cycles for the happy number sequences in base 8.
Base Puzzle
Age 11 to 14
Challenge Level
This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 .Octi the octopus counts.
Basic Rhythms
Age 16 to 18
Challenge Level
Explore a number pattern which has the same symmetries in different bases.
Binary Squares
Age 16 to 18
Challenge Level
If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?
Nim
Age 14 to 16
Challenge Level
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.
Code to Zero
Age 16 to 18
Challenge Level
Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.
It Must Be 2000
Age 7 to 11
Challenge Level
Here are many ideas for you to investigate - all linked with the number 2000.
Sometimes We Lose Things
Age 7 to 11
Challenge Level
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
NRICH is part of the family of activities in the Millennium Mathematics Project.