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# The Last Puzzle of the Night

Mapraputa Is
Leverager of our synergies
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Posts: 10065
"The Last" because I am not sure if my account will be locked by tomorrow
Warning:
If you are under 18 do not read this post!
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I was looking for new (more difficult) puzzles, and find one... Not really difficult, but trying to solve it was a lot of ... um... fun. Here is the original URL for those who can read Russian to prove that I didn't make it up.
This puzzle is interesting in that it has two symmetric formulations and two symmetric solutions. Milorad Pavic's "Dictionary of the Khazars" has analogous symmetrical form: the book "comes in two distinct editions, a male and a female", in many printings both of them can be read if you open the book from another side.
But I digress.
The Last Puzzle of the Night
Man's version
One night you were visited by three your girlfriends. All three are very, very pretty, so you really want to establish rather close relationships with all of them (in turn). The problem: 1) you know that there is a bad contagious disease in your neighborhood 2) you do not have any reason to trust any of your girlfriends, neither do they 3) you have only two condoms and all stores are already closed The question: how do you fulfil your goals?
Woman's version
One night you were visited by three your boyfriends. All three are very, very smart and good looking, so you do not mind to establish serious relationships with all of them (in turn). The problem: 1) you know that there is a bad contagious disease in your neighborhood 2) you do not have any reason to trust any of your boyfriends, neither do they 3) you have only two condoms and all stores are already closed The question: how do you fulfil your goals?
Notes to both versions:
Your solution should be susceptible of formalization, i.e. to be expressible as a mathematical formula. Washing/boiling wont work and no perversions please!

Jim Yingst
Wanderer
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Posts: 18671
The problem, as I see it, is that after the first "relationship" , the man and the woman are going to discover they have rather different and incompatible plans in mind for the remaining uses of the condoms.

Mapraputa Is
Leverager of our synergies
Sheriff
Posts: 10065
I won!
At last! I found a puzzle Jim cannot solve!
No wonder! No man can think logically in this situation. Oh well.

Jim Yingst
Wanderer
Sheriff
Posts: 18671
Just so we're clear, the problem I'm considering is the simultaneous solution of both versions of the problem. Which, sadly, does not seem to be possible. Ah well...

Mapraputa Is
Leverager of our synergies
Sheriff
Posts: 10065
I failed to see why solutions to both versions cannot happen simultaneously. Unless you imply that both solutions use the same set of condoms which is not required by the puzzle formulation.

Sameer Jamal
Ranch Hand
Posts: 1870
Use the first condom then take it off then put on the second one over it put one the first one then use it again take out the first one and then finally use the second one
Have a safe sex

Legolas
Greenhorn
Posts: 3
There are totally 4 sides of condom available for use between 4 people. So the idea is to use all the four sides.
Solution for the man's version.
For Woman #1 - Put Condom #2 over Condom #1. After the process, The outer side of #2 and inner side of #1 have been used.
For Woman #2 - Remove Condom #2 and use just Condom #1. After the process, the outer side of #1 is also used.
For woman #3 - Reverse Condom #2 and put it over Condom #1. Eureka!!!
Solution for the woman's version.
For man #1 - Put Condom #2 over Condom #1. After the process, the inner side of #1 and outer side of #2 are used.
For man #2 - Take out Condom #1 and use just Condom #2. After process, the inner side of #2 is also used.
For man #3. Reverse Condom #1 and out Condom #2 over Condom #1. Eureka, again!!!.

L!

Jim Yingst
Wanderer
Sheriff
Posts: 18671
I failed to see why solutions to both versions cannot happen simultaneously. Unless you imply that both solutions use the same set of condoms which is not required by the puzzle formulation.
Well, mostly because it's too easy if there are four condoms. I assumed that the two problems were two views of the same situation, with some information shared and some not. The man doesn't know about the other men; the woman doesn't know about the other women. (Not specifically anyway.) But if both man and woman each had a pair of condoms, then at least one of the problem descriptions should explain that "you have two condoms, and your partner has [at least one] condom". Instead, the problems clearly imply that there are only two condoms available.
Hmmm... OK, given that there are actually 3 men and 3 women in the vicinity, let's assume that all are equally promiscuous and wish to have, as Map says, "close relationships" with all 3 members of the opposite sex. One at a time. Nine pairings total among the group. What is the minimum number of condoms required to be able to do this "safely"? (If we pretend for a moment that the careful re-use of condoms described in the previous solution is "safe". :roll: )

Jamie Robertson
Ranch Hand
Posts: 1879
this one's easy...
for the first 2 use the condoms
for the last one, head to the kitchen for saran wrap and an elastic!
... or just leave one on for the entire day.

Michael Ernest
High Plains Drifter
Sheriff
Posts: 7292
I assume that a used condom is a used condom. If you can't trust any partner, and they can't trust you, it stands to reason both sides of a condom are used (and subsequently 'suspect') after one act. At least that would be the case 'in practice.' You theoreticians probably don't need to worry about that.

Jim Yingst
Wanderer
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Posts: 18671
True. Unless all actions are carefully observed by all parties. To ensure "safe" practices are observed.

Michael Ernest
High Plains Drifter
Sheriff
Posts: 7292
I think Sameer's got it, but I'm not sure I interpret it correctly. Therefore I *believe* I am restating it here.
Act I: Wear both condoms
Act II: Remove outer condom
Act III: Reverse outer condom and wear over inner
Doesn't sound like much fun for the guy, though

Jim Yingst
Wanderer
Sheriff
Posts: 18671
I couldn't decipher Sameer's solution at all - but you and "Legolas" have it.

Sandra Marti
Ranch Hand
Posts: 63
Originally posted by Michael Ernest:
I think Sameer's got it, but I'm not sure I interpret it correctly. Therefore I *believe* I am restating it here.
Act I: Wear both condoms
Act II: Remove outer condom
Act III: Reverse outer condom and wear over inner

I think what Sameer said is,
Act I: Use First condom
Act II: Wear Second condom and then wear First condom over it
Act III:Use Second condom
[ April 30, 2002: Message edited by: Sandra Marti ]

Corey McGlone
Ranch Hand
Posts: 3271
Originally posted by Michael Ernest:
Doesn't sound like much fun for the guy, though

What part of not having enough condoms for all the women that would like to have "close relations" with you doesn't sound like fun? (Or a great problem to have, at the very least?)
Corey

Jim Yingst
Wanderer
Sheriff
Posts: 18671
What part of not having enough condoms for all the women that would like to have "close relations" with you doesn't sound like fun?
Using Michael's described solution - the first part of Act III. Details left to the imagination - but there's a reason I've been using quotes around the word "safe".

Mapraputa Is
Leverager of our synergies
Sheriff
Posts: 10065
Originally posted by Jim Yingst:
OK, given that there are actually 3 men and 3 women in the vicinity, let's assume that all are equally promiscuous and wish to have, as Map says, "close relationships" with all 3 members of the opposite sex. One at a time. Nine pairings total among the group. What is the minimum number of condoms required to be able to do this "safely"?

This is a worthwhile problem for any deep thinker. I solved the easiest case: 2 x 2. These guys need only two condoms to establish 4 serious relationships. I still cannot prove that 3 x 3 would suffice with only 3 condoms... 4 condoms is obviously enough.
N x N problem is a real challenge. I think, this time Jim did construct the problem he cannot solve. Note that there is no direct correspondence between number of condoms * 2 = surfaces and number of close relationships (which from the woman's side are called "serious relationships"). For example, 8 condoms (16 working surfaces) are enough for 5 x 5 situation (25 serious relationships).
Jim, if I were you, I would check this source, maybe it will give some ideas.
[ April 30, 2002: Message edited by: Mapraputa Is ]

Anonymous
Ranch Hand
Posts: 18944
I wanna be this guy.....lucky bastard :-)

Mapraputa Is
Leverager of our synergies
Sheriff
Posts: 10065
There is an interesting phenomenon in topology called Klein Bottle. Kinda M�bius strips, but Klein Bottle is one-sided container. Now the question is: with a Klein condom, can you have unlimited number of relationships, or none?

Jim Yingst
Wanderer
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Posts: 18671
I'd say "none". Since a Klein condom would have only one side, it wouldn't really be a barrier to anything. Well, I suppose if you had one that was sufficiently flexible, you could tie a knot in part of it, effectively pinching it off. At which point it becomes like a normal condom with a funny knot attached to it, existing partly in the fourth dimension. (Which may or may not have other benefits, but I doubt it.)
Interestingly, while Klein condoms do not seem to be commercially available in our world, you can buy a reasonable 3-D approximation of a Klein bottle from these folks. My favorite is the Klein stein. While it seems to do fine holding liquids, that seems to largely depend on the fact that it's a rigid body, and they're able to keep the top "hole" reasonably far away from the liquid. Replace it with a flexible material, and it doesn't strike me as particularly safe. But as a beer mug, it's very . (Although it's evidently a pain to clean properly - don't put milk in it, or you may never get it out.)

Dirk Schreckmann
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Posts: 7023
At first, me thinks, "Hmm... \$80 bucks!" But then they won me over with Mapraputian Logic: "a trivial sum compared to the millions spent on asparagus."

Randall Twede
Ranch Hand
Posts: 4395
3
hmmm

Man's version
One night you were visited by three your girlfriends. All three are very, very pretty, so you really want to establish rather close relationships with all of them (in turn).

that sounds right

Woman's version
One night you were visited by three your boyfriends. All three are very, very smart and good looking, so you do not mind to establish serious relationships with all of them (in turn).

the learning channel said that is not what attracts women. according to them it should read

Woman's version
One night you were visited by three your boyfriends. All three have very, very good jobs, so you do not mind to establish serious relationships with all of them (in turn).

[ May 05, 2002: Message edited by: Randall Twede ]