### There are 19 results

Broad Topics >

Numbers and the Number System > Number bases

##### 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)?

##### 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?

##### 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.

##### 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.

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Can you create a Latin Square from multiples of a six digit number?

##### Age 7 to 16 Challenge Level:

A collection of games on the NIM theme

##### Age 11 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 winner is the player to take the last counter.

##### 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.

##### 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.

##### 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.

##### 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.

##### Age 14 to 16 Challenge Level:

Find b where 3723(base 10) = 123(base b).

##### 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.

##### 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.

##### Age 14 to 16 Challenge Level:

Have you seen this way of doing multiplication ?

##### 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.

##### 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?

##### 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?