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.
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
The number 3723(in base 10) is written as 123 in another base. What
is that base?
This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 .Octi the octopus counts.
There are two forms of counting on Vuvv - Zios count in base 3 and
Zepts count in base 7. One day four of these creatures, two Zios
and two Zepts, sat on the summit of a hill to count the legs of. . . .
A collection of games on the NIM theme
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.
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.
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.
How would you count the number of fingers in these pictures?
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.
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?
Here are many ideas for you to investigate - all linked with the
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.
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. . . .