Someone post a clever puzzle

Prefereably something very difficult, mathematical in nature, and quirky. This is the closest I will ever be to posting a personal ad.

Originally posted by royalchicken
Prefereably something very difficult, mathematical in nature, and quirky. This is the closest I will ever be to posting a personal ad.

State (using colourful but mathematically precise language) and prove Gowers' Dichotomy Theorem. 😛

Originally posted by Acolyte
State (using colourful but mathematically precise language) and prove Gowers' Dichotomy Theorem. 😛

'hereditarily indecomposable' 😕!

Check this out
OK lets begin
You are on a games show,
there are 3 doors
behind one door is a car and behind the other doors are nothing
You choose a door at random
the gameshow host opens one of the doors which you have not picked and reveals it to be empty.
He says you may change your choice to un opened door or stay with your original choice.

QUESTION

should you stay with your choice, change door or dosent it matter?

Originally posted by Brother Edwin
Check this out
OK lets begin
You are on a games show,
there are 3 doors
behind one door is a car and behind the other doors are nothing
You choose a door at random
the gameshow host opens one of the doors which you have not picked and reveals it to be empty.
He says you may change your choice to un opened door or stay with your original choice.

QUESTION

should you stay with your choice, change door or dosent it matter?

Well, switching doubles your chances of finding the car, but this puzzle has been posted here before, and we had a rocking good argument. Some silly fellow who calls himself 'Arbeiter' went particularly far in making an ass of himself 😉.

Originally posted by royalchicken
Prefereably something very difficult, mathematical in nature, and quirky. This is the closest I will ever be to posting a personal ad.

OK, TRY these two mathematical problems : -
(a) Evaluate the definite integral of SQRT( a + cos x ) .dx for x going from 0 to pi , where a > 1.
(b) Evaluate the definite integral of SQRT{ a^2 + (cos x)^2}.dx for x going from 0 to pi, where a not equal to 1.

Find the parametric forms (analytical expressions) in terms of the parameter a.


This is quirky and difficult and solvable.

Originally posted by sarathian
OK, TRY these two mathematical problems : -
(a) Evaluate the definite integral of SQRT( a + cos x ) .dx for x going from 0 to pi , where a > 1.
(b) Evaluate the definite integral of SQRT{ a^2 + (cos x)^2}.dx for x going from 0 to pi, where a not equal to 1.

Find the parametric forms (analytical expres ...[text shortened]... ons) in terms of the parameter a.


This is quirky and difficult and solvable.

Tsk,tsk...having us do your homework 🙂

Originally posted by royalchicken
Prefereably something very difficult, mathematical in nature, and quirky. This is the closest I will ever be to posting a personal ad.

Suppose you post a personal ad, get a reply, and set up a blind date.
Upon meeting your date you find that she is incredibly attractive, but
there's something about her that makes you think she has slept around
and may be disease infested. However, her stunning looks also empower
her with the ability to have been quite selective with her past lovers.

Suppose you receive a second reply from another respondent and set
up another blind date. This one is particularly unattractive. While she's
not the sort to win over any man she wants with her looks, you fear that
she may be disease infested too, since her looks are such that she would
have jumped at the chance to get any action at all in the past, without
exercising any selectivity.

Suppose you sleep with both women and find yourself with herpes
the next month.

Perform a Bayesian analysis to determine which woman was more likely
to have given you the disease. Your analysis should entail an estimation
of the likelihood that each woman was infected, a defense of those estimations
stating your assumptions and your confidence in them, and a proper conditional
analysis based on those estimations.

Dr. S

P.S. For extra credit, perform this marginal analysis. How many extra times would you have had to have slept with the woman you deem to be the non-culprit in order for your decision to switch? That is, if you had slept with one of them 10 time instead of one, how would that affect your conclusion.

Originally posted by DoctorScribbles
Suppose you post a personal ad, get a reply, and set up a blind date.
Upon meeting your date you find that she is incredibly attractive, but
there's something about her that makes you think she has slept around
and may be disease infested. However, her stunning looks also empower
her with the ability to have been quite selective with her past l ...[text shortened]... if you had slept with one of them 10 time instead of one, how would that affect your conclusion.

Tsk, tsk. Trying to get RoyalChicken to do your homework,
Doc. How dishonest!

Just phone call each of these 'hypothetical women'
and tell them they need to get tested. That would be
the chivalric thing to do.

Imagine, taking advantage of an innocent like RoyalChicken
to try to get him to figure out who likely gave you HSV. For
shame.

Nemesio 😉

Originally posted by DoctorScribbles
Suppose you post a personal ad, get a reply, and set up a blind date.
Upon meeting your date you find that she is incredibly attractive, but
there's something about her that makes you think she has slept around
and may be disease infested. However, her stunning looks also empower
her with the ability to have been quite selective with her past l ...[text shortened]... if you had slept with one of them 10 time instead of one, how would that affect your conclusion.

When I can be bothered to write the next entry in the Companion Thread on Bayesian inference/weight of evidence at FW, I will use this example rather than God, because there are fewer objections to it.

Here is one: Open your mind!

By the following rules:
1) in a line there is W ("omega&quot😉 points (W is infinity = alef zero).
2) in a 2D space there are W^2 lines.

How many circles and elipses there are in a 2D space?

Originally posted by TheMaster37
Tsk,tsk...having us do your homework 🙂

No ,I am not asking RC to do any home work. The questions do not occur in any textbook. Try solving it and you will immediately find out that these problems cannot be part of anybody's classwork or home work. Moreover I passed out of university some ten years ago.

Like RC, I enjoy solving quirky mathematical problems and it is bit natural that guys with similar interest, share their excursions in solving tricky puzzles.

Try it out, it is interesting. These definite integrals arose as a result of solving some other puzzles posted in this very forum.

Originally posted by sarathian
No ,I am not asking RC to do any home work. The questions do not occur in any textbook. Try solving it and you will immediately find out that these problems cannot be part of anybody's classwork or home w ...[text shortened]... f solving some other puzzles posted in this very forum.

I can only reduce them to some complicated stuff times some funny integrals involving a; I can't get a complete expression for them in terms of elementary functions.

Originally posted by yevgenip
Here is one: Open your mind!

By the following rules:
1) in a line there is W ("omega"😉 points (W is infinity = alef zero).
2) in a 2D space there are W^2 lines.

How many circles and elipses there are in a 2D space?

Note that there are W^2 points in a finite or infinite 2D space and that W^x = W where x is a finite positive number. I will ignore this second fact.
For each point in the plane, there is a 2D space (containing W^2 points) to the bottom and right of it (a quadrant). This space contains W^2 points.
2 points determine an ellipse or circle (by determining its minimal circumscribed rectangle). So for each point and each point below and right of it, there is an ellipse. Therefore, there are W^4 ellipses and circles.

Originally posted by Mouse2
Note that there are W^2 points in a finite or infinite 2D space and that W^x = W where x is a finite positive number. I will ignore this second fact.
For each point in the plane, there is a 2D space (containing W^2 points) southeast of it (for any arbitrary designation "southeast" that gives a quandrant). This space contains W^2 points.
2 points determine ...[text shortened]... cle (by determining its minimal circumscribed rectangle). So there are W^4 ellipses and circles.

Only W^3 circles: a circle can be specified freely by a point (2df) and a radius (1df) giving a total of 3 degrees of freedom.