Help!?

[Nicklez]

Hi, I'm new here and I was wondering if anyone could help?
I have a maths module due in soon, and I am seriously stuck on some questions:

King Arthur wished to marry off his daughter to one of the knights of his land. Being mathematical fo mind she set a problem for the knights
I invite all the knights of the land, place the seats in a circle numbering from one, Let the knights choose their seat. Say to the first "you live", to the second "Off with your head!" To the third "You live". To the fourth "Off with your head", and so on until only one knight remains, this will be the knight I marry.

So far I have drawn a *TON* of diagrams, and all I've found is that all of the "Winners" were sitting in odd seats.


The second question that I need help on is to do with trapezoidal numbers.
I need some help finding the rules for:
- Predicting the number of trapezoidal forms any number will have
- Which numbers can be represented by 'n' addends

A number is a Trapezoidal number if it is the sum of the consecutive positive integers. eg. 9=4+5 or 2+3+4

I've gotten as far as finding that all ODD nnumbers have 2 addends, and all multiples of three (excluding the number three) have got three addends.

If anyone could help me with this, or give any advice/links anything, it would be *really* greatly appreciated

[Nicklez]

I successfully finished the question about the trapezoids, but I still need some help with the knights one.

It says on my module that it has something to do with powers of two?
-Thanks, Nicki