Monday, August 20, 2012

Assassin Solution

As the old saying goes, there is more than one way to kill an iguana.  At least I think that's that way the old saying goes.

Well never mind.  There is more than one way to solve the Assassin in the Santa Lorena Plaza Problem.  I will list a few here.

Working Backwards:

As you may or may not recall in the last gory event there were 8 folks remaining.  Since each spree resulted in the demise of one third of the folks hanging around (once again there is no explaining why they didn't just run out of the plaza).  That means two-thirds lived through the incident.  Dividing by two-thirds is the same as mutiplying by three-halfs.  8 X 3/2 = 12.  Now just iterate the process two more times.  12 X 3/2 = 18.  And again.  18 X 3/2 = 27.  Besides the assassin himself, there were 27 folks, so the answer is 27 or 28 depending on how you interpret 'originally'.

Forward Using an Equation:

Let X be the original amount of people in the plaza (not including our assassin).  After the first killing, there would be X - X/3 = 2X/3 people remaining.

Of these (after his latte of course) the killer wiped out a third more or 2X/9.  The new amount left would be 2X/3 - 2X/9 = 4X/9.

After his round of pilates, the assassin took out one-third more or 4X/27.  Subtracting again we get
4X/9 - 4X/27 = 8X/27.

But this equals 8 people.  Thus 8X/27 = 8.  Solving for X we get X = 27

I think I'm going to quit here.  If anyone used a third method, (say a chart) please fell free to post it on my Facebook page.  You will be appropriately lauded.

I will recognize and award the un-prizes there as well.  I hope you had as much fun with this problem as I did.

Thanks for playing.