Surviving the Desert - Can You Choose Your Fate?

[AntonVrba]

The cannibal logic teasers reminded me of this one:

The scene: you are captured in the middle of a desert, it is the middle of the day, sun shining, and you are all sweaty, sticky, thirsty etc. The smell of camels is overwhelming and the desert dust is causing your eyes to sting.

Your fate: Your capturers have told you, in the leather bag are 9 (yes nine) black billiard balls and one white cue ball. You will be be blind folded and then you can choose one ball. Should it be white you are free to go, should be black ...

Your last wish: You have one wish which will be fulfilled - what is it so you can go free.

 

[marcus]

The cannibal logic teasers reminded me of this one:

The scene: you are captured in the middle of a desert, it is the middle of the day, sun shining, and you are all sweaty, sticky, thirsty etc. The smell of camels is overwhelming and the desert dust is causing your eyes to sting.

Your fate: Your capturers have told you, in the leather bag are 9 (yes nine) black billiard balls and one white cue ball. You will be be blind folded and then you can choose one ball. Should it be white you are free to go, should be black ...

Your last wish: You have one wish which will be fulfilled - what is it so you can go free.

I will ask them to put the balls out on a flat surface in the sun for a few minutes, and then let me choose.
the white ball will be cooler to touch.
so even though I am blindfolded I will be able to feel which is the white ball.[/color]

 

[AntonVrba]

Marcus, congratulations

 

[BicycleTree]

Or, you could just wish to be let free.

 

[Alkatran]

I was going to wish for all the balls to be white.

 

[DaveC426913]

Considering the number of answers that used a metaphysical form of "wish" (i.e. genie in a bottle kind), I suggest altering this puzzle as follows:

"Your captors will grant you one last reasonable request."

 

[Rahmuss]

Hmmm... I guess it depends on how big this desert is, and if anything else is around. I think I'd rather be a captive, than someone who died of thirst and head and have my body eaten by who knows what in the middle of the desert. So I'd be for hoping that I wouldn't get the white ball.

 

[kleinwolf]

May I ask a stupid question, is the fact that the number of balls is 9 important ?

 

[Galileo]

You could, I suppose have 99 black balls. It would look mighty funny when you're busy for an hour trying to find the white ball.

 

[kleinwolf]

Yes...so what is the dependence of the temperature of the black balls and the white ball with respect to to time ??

Is just the "speed" of temperature elevation smaller by the white ball, but the saturation temperature are the same (ambient temperature) or is the final temperature higher by the black ball (not higher than the ambient, but than the white's one) ?

Do we assume the balls have same mass, same volume (and same calorific capacity ?)only the color is important. So that in fact the temperature is the result of a dynamic equilibrium, something like that...?

With my first thought on this, then you should be quite quick, because if the power transfer is proportional (coefficient dep. on the color) to the difference of temperatures between the ambient and the ball, then the final temperature is the same for both balls...How could one modelize the fact that the white ball could have a lower temperature at equilibrium (i.e. after a long time) ??

In fact I'm completely out of the reality, because the temperature of the black ball, at least,, will be higher than the temperature of the air around (a bit away from the surface)...


Yes...in fact I'm just thinking if the power transmission du to conduction is prop. to the differences of temperatures...Then instead of taking Stefan's law for the EM radiation power, one can at first simplify with a constant (eerk...it's because I don't want to factorize 4th order polynomials) :

$$P_{in}=(1-\lambda)\alpha S$$ (S=surface)
$$P_{out}=\lambda\alpha S$$ for radiation
$$P_{cond}=\beta (T_a-T)S$$ for conduction

so that : $$mc_s\frac{dT}{dt}=P_{in}-P_{out}+P_{cond}$$

hence $$T(t)=T_a+(1-2\lambda)\frac{\alpha}{\beta}-Ae^{-\frac{mc_s}{\beta S}t}$$

hence $$T(\infty)=T_a+(1-2\lambda)\frac{\alpha}{\beta}$$

where $$\lambda=0->black,\lambda=1->white$$...


I'm just playing around...I wonder if taking the EM power radiation instead of constant, one could get oscillating behaviour around the equi. temp ??

What about the EM power being send to the ball ??