Number bases

problem
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?
problem
Back to basics

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

The number 3723(in base 10) is written as 123 in another base. What is that base?
problem
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.
problem
Basic rhythms

Age

16 to 18

Challenge level

Explore a number pattern which has the same symmetries in different bases.
problem
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)?
problem
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.
problem
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.
problem
It must be 2000

Age

7 to 11

Challenge level

Here are many ideas for you to investigate - all linked with the number 2000.
problem
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.