CONTINUOUSWAVE

This may be something fun to work on over the holidays, a little puzzle.

Suppose you are on a North-Channel-of-Lake-Huron cruise in a big fleet of Boston Whaler boats, 25-boats in total. The fleet comes to a marina which has exactly 25-slips, all unoccupied and waiting for the fleet to arrive. The fleet has made reservations, and every boat in the fleet has been pre-assigned a slip. There is a little problem, because the first boat in the fleet to enter the marina has lost the email with his slip reservation. He figures, what the heck, "I'll just take a slip at random," and he does.

You are the last boat in the fleet to arrive at the marina, and all 24 other boats are already in slips. What are the odds that your assigned slip will be vacant when you enter the marina?

Assuming all the other 23 either went to their assigned slip or traded with the first guy if he had taken theirs, I'll say 50/50 odds...

If they all did what he did, odds would be much lower :)

Tim,

Good solution.

Or just change the numbers on the slip and you will be in yours 100%

I adapted this puzzle from the more well-known airline seat puzzle, whose solution is explained at:

https://www3.nd.edu/~dgalvin1/Probpuz/probpuz3.html

I have read this solution a dozen times, but I still am having trouble seeing it clearly.

I think the simplest way to understand this puzzle is to consider the options for the first boat; there are three possibilities for the slip the first boat takes:

--he takes the slip he was supposed to take, by chance; if this happens, everyone else gets their assigned slip;

--he takes the slip you were supposed to take; everyone ahead of you gets their assigned slip, and when you arrive the only slip left is the one the first boat should have taken;

--he takes some other slip, not your slip and not the one he was assigned.

Consider that the only option that makes another boat have to take a slip other than their assigned slip is the third option for the first boat; what this means is that your slip and the first boat's slip must STILL BE OPEN (because all the rest of the boats took their assigned slips). So the choices for that boat are:

--he takes the slip the first boat was supposed to take;

--he takes your slip; or

--he takes some other boat's slip.

The odds he will take your slip or the first boat's slip are the same. If he takes another boat's slip, nothing really happens to the odds of your slip being taken because it just pushes the chance of your slip being taken down the line to the next boat that comes into the marina and finds their assigned slip is already taken. The outcome is the odds your slip will be taken or not are 50-50.

I asked my 10 year old granddaughter who is a math wiz for help on this puzzle. She sez that the odds are 25 to one against the first boat pulling into the right slip. As the boats file in the owner of the slip that the first boat pulled into will tell the occupant, " hey dude, your in my slip. lets move it. So then the first boat leaves and idles around outside the marina until all the slips are filled. Then he takes the one empty one. You, as the last one in pass then idling boat pull into your appointed slip, unaware that anything was amiss. She said that that is the way it should work in real life anyway, but nowadays the boater who lost his email maybe a real jerk about having to move and may pull a gun from the console.
,

Binkster wrote:I asked my 10 year old granddaughter who is a math wiz for help on this puzzle. She sez ...

I see that skill at math puzzles runs in your family. And you've passed on to your granddaughter some important life lessons.

The airplane seat version of this puzzle was "The Puzzler" on an old episode of Car Talk. Here is Tom and Ray's solution:

https://web.archive.org/web/20050301133732/http://www.cartalk.com/content/puzzler/transcripts/200440/answer.html

The odds are nearly 100-percent that the 24th boat will:

--get the slip furthest from the public bathroom and showers
--get the slip closest to the gas dock and pump out machinery
--get the slip missing two cleats
--get the slip closest the the Bayliner cruiser leaking oil and playing ABBA recordings all night.

David, --I laugh aloud-- and true 50 50 chance