13 Jul 2013

Prize Maths Quiz: King Arthur and the Round Table Puzzle (PMQ27)

King Arthur was slumped on his throne, glaring at his squabbling knights. Time for another quest, he thought.

"Right! All of you sit down! Time for one of you to go in search of the fabled Grail."

The knights groaned; it echoed round the chamber, sounding like it had been emitted by a giant bear. As the knights shuffled their way to the Round Table, Sir Rod the Obtuse spoke what was on all their minds.

"Great King, how will you decide which of us gallant knights shall set forth on this onerous quest?"

"I think 'gallant' is exhibiting a rash of pride, Sir Rod. Nevertheless, to answer your question, I shall use the usual method. All I am willing to divulge is that I shall be using... two dice."

The consternation that followed was merely a manifestation of their collective inner turmoil. Mathematical acuity had never been on the list of personal qualities necessary for knighthood. Merlin had the brains, and most knights were more than happy not to tread on Merlin's turf. Amidst the anxious clatter, Sir Rod the Obtuse had a quiet word with Merlin, who was taking an aloof stance to the proceedings. Merlin nodded in agreement and the two men parted.

The Round Table was designed so that the chairs were numbered in sequence 0, 1, 2, 3, ... n, where n was the number of knights present. The chair numbered 0 was always empty, ready for the return of a knight who would finally find the Grail. King Arthur sat on an unnumbered throne.

Once all the knights were seated, Arthur would take out some dice from a box and roll them to get a number, k. Arthur would then count around the Table, starting at 0, and eliminate the knight seated in every k-th chair. He would continue in this fashion until only one chair was left. If the last remaining chair was the 0-chair, then nobody would set out to find the Grail - but King Arthur still enjoyed the sport of making his knights sweat!

For example, if Arthur rolls a 3, and there are only 4 knights present, then the chairs would be numbered (0, 1, 2, 3, 4) and sequence of eliminated chairs would be (2, 0, 4, 1, 3). The knight sitting in chair number 3 would be packing his bags and saddling his horse.

On this particular day, there were 12 knights present and King Arthur chose to roll two standard six-sided dice. Sir Rod the Obtuse had no intention of riding off to his doom, nor of returning to find himself dispossessed. Which numbered chair should he sit in to avoid being chosen for the Grail quest?

You may discuss the question below, but no full answers, please, until the competition has closed!

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How to Enter

Send your complete solution by email to pmq27obtuse@giftedmaths.comThis email address shall be removed after the competition closes to avoid spam. This PMQ27 competition closes on MONDAY 15 July at 23:59 GMT - one extra weekday from now on.

The Prize

The prizes for this PMQ are 3 free places in our Online Maths Club for ONE YEAR. The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received. All winners can have their name posted and a link to their own online profile at their favourite social network or their own blog.

Quick Rules

Look at the expanded rules on our PMQ page.
Anybody can enter our Prize Maths Quiz; adults and students.
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