The Assassin Problem 3

Having a look at some of your solutions to The Assassin Problem (original video here http://www.youtube.com/watch?v=crkeHTaVOyY )

My solution video here http://www.youtube.com/watch?v=7d6E2oJ4-u0

Matt Parker's video solution here http://www.youtube.com/watch?v=kDl_MXWmlqs

The vast majority of solutions, including all solutions in this video (except mine), are the same underneath.

Mathematically speaking we say they are 'isomorphic', in that they may look different on the surface but they possess the same mathematical structure underneath.

The majority involved assigning each player a number (either physically by position, or by assigning a number to each name) and then performing x+1 mod 8 (adding one to each number, where the numbers wrap round back to 1).

Essentially, this is what an 8-cycle is, so they all answer the question given. However, how they perform this x+1 operation, practically and secretly, is what makes them different.

Some solutions found ingenious ways to make use of a different shift, like x+2, x+3, x+4 etc (In fact this is the solution the original poster, Tom, had). However, if the shift divides the number of players then this will not make one full cycle, but instead will break up the players into subsets. So in our main example, since 2 and 4 both divide 8, these shifts do not make one complete cycle.

My solution works on a completely different mathematical principle, which I did on purpose - I am meant to be the expert afterall. It uses an idea called conjugation; a permuation sandwiched between a function and its inverse will return a permuation of the same cycle type. The shuffling of the names and looking to the next name down in the pack is the x+1 idea again, but that is sandwiched between the idea of making pairs, with pairs being self-inverse.

Giving each name a number is a bijection (a labelling). Which number kills which other number is the structure, with most answers having an x+1 structure, with the exceptions mentioned above.

Category:

Education

Tags:

• maths
• math
• mathematics
• problem
• puzzle
• game
• assassin
• james
• grime
• singingbanana
• matt
• parker
• standupmaths
• yakawow

[scotland7yard]

Bet you went through the trouble of making this whole video just for the running bit (cuz it's fucking class!!)

[singingbanana]

@scotland7yard Busted!

[smilingxxpasta]

Oh no! I can't click your face James! @_@~

[singingbanana]

@smilingxxpasta You should be able to. The annotation is there if you hover.

[TheOriginalThwomp]

I sense sexual tension!

[PoketoMtg]

Isn't the 4th one still having a problem as it is not repeatable with out writing out a new set of cards? I found the stack then looking at +1 a good idea, but using a stack of blank cards underneath (with the number still on top) to hide information from anyone else.

[Theraot]

@kamiakin5 the program is third party, on the original problem it is stated that it must be solved without need of that. You'll see, this kind of problem has application in developing secure protocols [or on multithreading], and this was meant to be without a centralized server, on the lines of p2p. That server sending mail is a problem for privacy if not worst. The server would have the upper hand to manipulate (hack) the situation. Even if not, the developer of the program would be able to.

[Theraot]

@Jack4liverpool what if you open your eyes? they would not notice cuz they have eyes closed. hmm... unless they were cheating too.

[Theraot]

that's really a high quality scissor that can cut arbitrary number of cards.

[CakesnakeFilms]

when i was 14 i went on a robotics engineering course at imperial college london, and this guy was one of the proffessors on it.

[Jack4liverpool]

I'm not a hater or anything, infact I think these videos are absolutely brillliant, but I don't understand how thesingingnerd's solution would only really work in a frictionless vacuum? I'm probably just overlooking something but it would be great if you could explain that to me, thanks.

[fredrocks222]

What if there were 100 players, sounds pretty hard to cut 100 cards

[fredrocks222]

I'm not in my underwear! I'm naked thank you very much

[geeta172]

u can just cut it anywhere...the 8 cycle would still remain...ryt?

[kamiakin5]

I know this is much later, but if you are having say 100 people, wouldn't it be more efficient if you just use a program to randomly fill slots 1 to 100? then just email each person their target at a specified time? ie, have a program that automatically sends the email after all players have signed up with their name and address.

Now if picking up is pertinent, each person could create a password as well. to look on after everyone has signed up.