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| Do you enjoy riddles? |
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| Total Votes : 5 |
Lintra
Elf Friend
Joined: 23 Apr 2002
Posts: 9448
Location: Bermuda, the triangle place with SANDY BEACHES |
quote:
Originally posted by Michael C
The No Vacancy problem: If the hotel must serve an infinite number of forrest people they will never have time to serve you, so my guess is that you can't get a room!
I went looking back over old posts trying not to duplicate, but I thought a new riddle would be fun.
Good answer on the Tractor Beam. Must be correct (drove the Tractor over the ice).
No Vacancy: I was going to bring this one up, but you beat me to it... my logic is as follows:
Z = Set of *all* integers is infinite and people are discrete units, and therefore integer like (it is refered to as countably infinite) since you are just another integer, there is a room for you. Mapping is as follows:
f = set of all forest people. f(i) = forest person i, zero indexed. Lim as i -> inf = Z
g = set of all forset people + you where g(0) = you and g(1) = f(0).
lim as i -> inf g = Z therfore there exists a room for you.
for the next problem (no vacancies)
Q = Set of *all* rational numbers if q in Q then q = a/b where a,b in Z and b <> 0. Q is also countably infinite, but Z in Q & Q not in Z and Q is infinite, in fact there are Z Z's in Q since
1, 1 + 1/2, 1+1/3...1+1/z is in Q,
2, 2 + 1/2, 2+1/3...2+1/z is in Q,
.
.
.
z, z + 1/2, z + 1/3...z+1/z is in Q,
so there is room for many infinities in this hotel!
Last edited by Lintra on Mon May 13, 2002 7:03 pm; edited 1 time in total |
Mon May 13, 2002 4:51 pm |
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Lintra
Elf Friend
Joined: 23 Apr 2002
Posts: 9448
Location: Bermuda, the triangle place with SANDY BEACHES |
I forgot to point this out...
There is problem with adding an additional point to an infinity. Here it is:
Make the following construct:
a circle "C" with its south pole touching (tangent to) the real line "R" at 0.
Then draw a line from the N pole through the circle through the line.
This assigns 1 point on R for each point in C. It is a one to one correspondence...except for the north pole. A line just through the north pole (tangent) is parellel to R. Where do tangent lines meet? At infinity.
A layman's description of this is "Drop an extra point into the real line, and it curls up into a circle" or "the circle = the real line + 1 point".
I don't believe it is relevent to the prior discussion, but then I am 20 years out of practice  |
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Mon May 13, 2002 6:05 pm |
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Lintra
Elf Friend
Joined: 23 Apr 2002
Posts: 9448
Location: Bermuda, the triangle place with SANDY BEACHES |
This riddle is "Three's a Crowd"
"After solving the riddle of the three wise folks, three scoundrels claim to be the smartest in the country. So you decide to give them a challenge. Suspecting that the thing they care about most is money, you give them $100 and tell them they are to divide this money observing the following rule: they are to discuss offers and counter-offers from each other and then take a vote. Majority vote wins.
Sounds easy enough... now the question is, assuming each person is motivated to take the largest amount possible, what will the outcome be?
Note: careful... if the answer were that they split it 50% / 50% / 0%, or 1/3 / 1/3 / 1/3, it wouldn't be a riddle! "
As far as I can see this is what happens:
Remember, the only rule is to increase wealth (you can not voluntarily decrease it).
After one round A+B agree to vote together and split the pot. So round end of round one the amounts are 50-50-0 (A-B-C)
Then a offers to split B’s amount with C if C votes with him, so end of round two the amounts are 75-25-0 (A-C-B)
Then C offers to split the 75 with B, the best a can do is offer to give C’s 25 to B so B takes C’s offer. End of round 3: 63.5-37.5-0 (C-B-A).
Round 4 and later, the one with the second most offers to split the most with the guy with 0. This is an infinite series with an end result 2/3-1/3-0, but no one person gets the 2/3, it is constantly shifting around.
The technical proof is let x_i = max amount in round i
Then in round i the guy with 0 will get x_i/2 leaving the rest for the winner so
x_i = 100 – x_(i-1)
If you extend this you get
x_i = 100(1 – ½ +1/4-1/8+1/6-1/32+...+x_(i – j)/2.
lim as x --> inf of x_i = 100(1 – ½ + 1/4-1/8+1/6-1/32+...)
= 100 (1/2 + 1/8 + 1/32 +...+ (1/2)^(2n+1) + ...
= 100 sum( ½^(2n – 1))
= 100 * ½ * sum( ½^2n)
= 50 * sum (1/4^n)
= 50 * 1/(1-1/4) a general rule (I can prove it if you wish)
= 50 * 4/ 3 = 66.66666
I played a little fast and loose with summation signs and limits, hoping they'd be obvious (this is not a great word processor!). |
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Mon May 13, 2002 7:47 pm |
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Potentated Knight of Ni
Protector of the Realm
Joined: 20 Apr 2002
Posts: 259
Location: Somewhere lost in Canada (I Know Where I am Not) |
I never knew that we had so many smart people on RPGDot (expluding moderators  ).
It is not fair that Lintra can solve all of the problems so easily.
--(for he/she is an acutary )
_________________
 We (me, myself, and I) are the the Knights who say "Nee"!=Member of The Nonflamers' Guild= |
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Mon May 13, 2002 9:12 pm |
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Michael C
Black Dragon
Joined: 09 Jul 2001
Posts: 1595
Location: Aarhus, Denmark |
Regarding the "No vacancy" riddle. I agree that you through math. can prove that there is a room for you, but the fact that there are an infinite amount of forrest people before you in line, you will never get to the counter and order that room. |
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Tue May 14, 2002 7:10 am |
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Michael C
Black Dragon
Joined: 09 Jul 2001
Posts: 1595
Location: Aarhus, Denmark |
Taking the first link (random riddles) from original page. The No.1 riddle where a 40 pounds rock has been broken into 4 uneven pieces which each weight a certain amount, so you can use a scale and messure any amount between 1 and 40 pounds (hole numbers), with only these 4 stones.
I found if the 4 stones weight 1,3,9 and 27 pounds, then it's possible! |
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Tue May 14, 2002 11:53 am |
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Michael C
Black Dragon
Joined: 09 Jul 2001
Posts: 1595
Location: Aarhus, Denmark |
No.3 riddle on random riddle page: Solution is letter "M". Easy one! |
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Tue May 14, 2002 11:55 am |
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Lintra
Elf Friend
Joined: 23 Apr 2002
Posts: 9448
Location: Bermuda, the triangle place with SANDY BEACHES |
quote:
Originally posted by Michael C
Regarding the "No vacancy" riddle. I agree that you through math. can prove that there is a room for you, but the fact that there are an infinite amount of forrest people before you in line, you will never get to the counter and order that room.
I like your approach, it is clean a simple (and I would not have thought of it  ). The problem is the riddle. It states
"In the forest, a hotel has an infinite number of rooms. An infinite number of forest people arrive and each takes a room. So far so good. Now you would like a room. "
So each forest person has a room already. The question is if there is a room for you.
Also
M is good
The poundage on the rocks follows the pattern
1,
3 = (1)*2 + 1,
9 = (1+3)*2+1,
27 = (1+3+9)*2+1
81 = (1+3+9+27)*2 + 1
etc
Work was slow yesterday and looks to be slow today. I printed out a list of the riddles what we have not answered yet and am working my way down the list. Would you me to post it? |
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Tue May 14, 2002 12:17 pm |
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Lintra
Elf Friend
Joined: 23 Apr 2002
Posts: 9448
Location: Bermuda, the triangle place with SANDY BEACHES |
quote:
Originally posted by Potentated Knight of Ni
...It is not fair that Lintra can solve all of the problems so easily.
--(for he/she is an acutary )
Not as easily as you might think! Michael C got the Eat&Run Riddle, and Yog Sothoth got the three dots  |
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Tue May 14, 2002 12:27 pm |
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Michael C
Black Dragon
Joined: 09 Jul 2001
Posts: 1595
Location: Aarhus, Denmark |
Lintra: Yep a remaining list of riddles would be fine!
BTW The solution on No.4 riddle in (random riddle) is: "Nothing". Nothing is stronger than god, nothing is more evil than the devil etc. |
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Tue May 14, 2002 12:58 pm |
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Michael C
Black Dragon
Joined: 09 Jul 2001
Posts: 1595
Location: Aarhus, Denmark |
Lintra: Your formula used for the 4 rocks is working and probably the most correct one, I just used the simple algorith nx3 to find the next number.
Ex.
1
1x3=3
3x3=9
9x3=27
27x3=81
81x3=243 and so on! |
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Tue May 14, 2002 1:06 pm |
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Lintra
Elf Friend
Joined: 23 Apr 2002
Posts: 9448
Location: Bermuda, the triangle place with SANDY BEACHES |
quote:
Originally posted by Michael C
Lintra: Yep a remaining list of riddles would be fine!
BTW The solution on No.4 riddle in (random riddle) is: "Nothing". Nothing is stronger than god, nothing is more evil than the devil etc.
Good ans on nothing, and here is the list- I think it is complete:
Three Dots - Done
Hat-trick - Done
Three's a Crowd - Done
Auction Action - Done
Ties that Bind
Hats Off
Open Door Policy - Done
Trouble in River City - Done
Timing is Everything
Light Bridge - Done
Flight Plight - Infinite series
Lazy Susan
Lying Defeeted - Done
No Vacancy - Done?
No Vacancies - Done?
Apairantly Not
Sailor's Delight
Eat and Run - Done
Tractor Beam - Done
Enlightenment
Ashpynxiated - Done
Heads Up
I had to edit this...while the text entry screen understands tabs they don't show up properly when submitted 
PS - I had totally missed that you were using powers of 3! I got there using the combination approach. There is a number theory theorum in there somewhere, but I don't feel up to digging it out  |
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Tue May 14, 2002 1:11 pm |
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Yog Sothoth
The All in One
Joined: 01 May 2002
Posts: 1086
Location: Between Space and Time |
quote:
Originally posted by Michael C
Lintra: Your formula used for the 4 rocks is working and probably the most correct one, I just used the simple algorith nx3 to find the next number.
Ex.
1
1x3=3
3x3=9
9x3=27
27x3=81
81x3=243 and so on!
I don't understand what does it mean the "to an accuracy of one pound" in the text of the riddle... how could you measure 7 pounds for example?
(i'm studing hard and i'm "out of work" with my mind... now i understand only the meaning of numbers in civil prodecure code articles... TILT  )
_________________
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=Memberof the 6thHouse=
=Member of the SportsFans Club=
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Tue May 14, 2002 2:15 pm |
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Lintra
Elf Friend
Joined: 23 Apr 2002
Posts: 9448
Location: Bermuda, the triangle place with SANDY BEACHES |
With a simple balance put the 3 lb wgt on one side and the 9 and 1 on the other, the difference is 7 lbs. |
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Tue May 14, 2002 2:34 pm |
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Yog Sothoth
The All in One
Joined: 01 May 2002
Posts: 1086
Location: Between Space and Time |
ops! there was a balance too... i never noticed sorry
_________________
=Member of the NonFlamers' Guild=
=Memberof the 6thHouse=
=Member of the SportsFans Club=
=Ex-Baron of the RPGDot Shadows= |
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Tue May 14, 2002 2:36 pm |
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