Number bases

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Learn about number bases

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.
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The knapsack problem and public key cryptography

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.
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A story about absolutely nothing

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.
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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.
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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?
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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.
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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)?
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Basic rhythms

Age

16 to 18

Challenge level

Explore a number pattern which has the same symmetries in different bases.
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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.
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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.