Mathematics question?

Question

KING ARTHURS KNIGHTS

king arthur wished to marry off his daughter to one of the knights of his land. Being mathematical of mind she set a problem for the knights.

"invite all the knights of the land"
Place the seats in a circle numbering them from one.
let the knight choose their seat
Say to the first "you live"
Next " off with your head.
the third: you live

and so on until only one knight remains.
this will be the night i marry

which seat would you choose if you were a knight wishing to marry the princess.

does the number of seats make a difference????


( how many knights are there because the question doesnt say)

Answer 1

You need to use objects (pennies, blocks whatever) to represent the knights and act out the problem collecting data until you can form your strategy. I got the information below from this web site: http://www.pasd.wednet.edu/school/mathWASL/hsg.htm

Strategy: Act out the problem or use objects (and collect some data) This is a hard problem. Use it only if you can devote several days to it. If there are n knights, you get the right seat number by subtracting off the largest power of two strictly less than n and then multiplying by two.

This is a fictionalized historical problem. King Arthur wanted to decide who was the fittest to marry his daughter, and chose this method. When all his knights were seated at the round table, he entered the room, pointed to one knight, and said: "You live." The knight seated next wasn't so fortunate. "You die," said King Arthur, chopping off his head. To the third knight he said: "You live," and to the fourth, he said: "You die," chopping off his head. He continued doing this around and around the circle, chopping off the head of every other living knight, until just one was left. This remaining knight got to marry the daughter, but, as legend goes, he was never quite the same again. Find a pattern so you can predict where to sit (to live) no matter how many people are seated in the circle. Explain your answer in detail.


Good Luck!

Jen

Answer 2

Since the First gets too Live,
and the Next Dies,
and the Third Lives,

This means that the Number of Kights is 2 or 3.

In the case that only ONE Lives, then there could only BE 3 Kights!!

Example: If there were 2 Knights, then;
1st Lives,
2nd Dies,
1st Lives,
2nd is Dead, so next..
ONLY knight Left dies!! NOONE!! : (

If there were 3 Knights, then;

1st Lives,
2nd Dies,
3rd Lives,
1st Dies,
2nd is Dead, so next one...
3rd lives....!!

Answer 3

the first.

Answer 4

My guess is that it has something to do with Fibonacci Numbers.