Number bases

problem
Favourite

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
Favourite

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.
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

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?
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

Basic Rhythms

Age

16 to 18

Challenge level

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

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.
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

Back to Basics

Age

14 to 16

Challenge level

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

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.