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Resources tagged with Number bases similar to Weekly Challenge 35: Clickety Click and All the Sixes:

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Broad Topics > Numbers and the Number System > Number bases

Binary Squares

Stage: 5 Challenge Level:

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?

Balance Power

Stage: 3, 4 and 5 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?

Stage: 2, 3, 4 and 5

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.

Nim

Stage: 4 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.

Napier's Location Arithmetic

Stage: 4 Challenge Level:

Have you seen this way of doing multiplication ?

More Secret Transmissions

Stage: 5 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?

Nim-like Games

Stage: 2, 3 and 4 Challenge Level:

A collection of games on the NIM theme

Latin Numbers

Stage: 4 Challenge Level:

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

Knapsack

Stage: 4 Challenge Level:

You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.

Nim-interactive

Stage: 3 and 4 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.

Secret Transmissions

Stage: 4 Challenge Level:

How can Agent X transmit data on a faulty line and be sure that her message will get through?

Basic Rhythms

Stage: 5 Challenge Level:

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

Phew I'm Factored

Stage: 4 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.

Composite Notions

Stage: 4 Challenge Level:

A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.

Binary Sequences

Stage: 5 Challenge Level:

Show that the infinite set of finite (or terminating) binary sequences can be written as an ordered list whereas the infinite set of all infinite binary sequences cannot.

Stage: 3, 4 and 5

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.

Code to Zero

Stage: 5 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.

Guesswork

Stage: 4 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.

Back to Basics

Stage: 4 Challenge Level:

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

The Knapsack Problem and Public Key Cryptography

Stage: 5

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.