Tuesday, 3 June 2014

The Perplexing King Arthur Problem

I first came across this problem when working on implementing the NZ Maths Curriculum in the 1990's.  We used with up primary and secondary teachers as the type of complex problems the curriculum was encouraging.  I have used it regularly and found most students find it challenging and come up with all different ways of solving, or at least trying to solve.  I hope your students find it equally challenging and motivational.

King Arthur had a problem.  His beautiful daughter, Catherine, loved mathematics so much that she spent most of her time solving problems, making geometric designs, and playing with numbers.
When it became time for Catherine to marry, she told her father that there was one requirement for a husband: he must love mathematics (or at least like it a lot.

King Arthur loved his daughter so much that he decided the best man to marry his daughter would be one of the Knights from the Round Table, but he had never heard any of them talk about mathematics.   King Arthur decided that the best way would be for Catherine to set a problem for the Knights and the Knight who solved the problem would be the man to marry his daughter.

Catherine spent weeks developing a maths problem that would ensure she married a Knight who was also a mathematician.  She eventually came up with the problem and said to her daddy that he could give it to the Knights and in a months time they could come back with their solutions.

Catherine explained, “Suppose 24 knights came to a meeting of the Round Table.  And suppose the 24 chairs are numbered in order, so that everyone knew which was chair one and which order they are numbered. 
Father you then take your sword and point to the first Knight and say- You Live!
You then point to the second knight and say, “you Die’ and chop off his head.
To the third knight you say you live and to the fourth you say “You Die,” You carry on around the table chopping off the head of every other living Knight until there is just one left sitting.  That is the Knight I will marry!”

“Catherine, I would then only have one knight left to help defend me and you!”
“Don’t be silly Daddy, this is a maths problem and you wont really chop of their heads”
“What happens if 24 Knights do not turn up”
Catherine giggled, That’s the real point to the problem, the Knight of my dreams will only know he has solved this problem if he knows where to sit for any number of chairs. I’ve been working on this problem and there’s a marvelous pattern for the solution!”

Which seat is the right one when there are 24 Knights at the Round Table?
Can you find a pattern for predicting which is the right seat for any number of chairs?
Hint solve a simpler problem first!

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