Riddles, brain puzzles and mathematical problems

[FlawlessHappiness]

The "game" was fun, but I suck at math-proofs

[BAndrew]

This is a classic. Some of you might know it.


We have 10 containers. Each container has a different type of gas. You know that the gases weight the same, except for one which has double the weight from the other gases. You want to find the heavier gas. You don't know where it is (i.e. you don't know in which container it is). You have a special electronic scale at your disposal, but it has enough energy for only one weighing. You can weight a combination of gases and you can weight the same gas (from the same container) multiple times. The only restriction is that you must find the heavier gas in only one weighing.

For example let's name the gases a,b,c,d,e,f,g,h,i,j (each gas from the corresponding container)

We can in one weighing calculate the value/weight of 2a + b + c +d + e + f + g +h + i + 3j or whatever combination we want.

[FlawlessHappiness]

Could you weigh 2a+3b+4c+5d+6e+7f+8g+9h+10i+11j

Then figure out what it would be if all gasses weighed the same.

Subtract that from the actual number, and from then on figure it out?

[BAndrew]

Could you weigh 2a+3b+4c+5d+6e+7f+8g+9h+10i+11j

Then figure out what it would be if all gasses weighed the same.

Subtract that from the actual number, and from then on figure it out?

Of course. That's actually the solution! Congratulations!

NOTE: any combination of the form:
k*a + (k+1)*b + (k+2)*c + ... + (k+9)
would do (k >0 and is an integer)

[BAndrew]

About Rainfroge's problem:
My proof was wrong or at least incomplete because it has two critical mistakes that I can't "fix". So the problem remains open.

[Romulator]

This has been circulating around imgur lately.

Spoiler below!

If you want to give it a serious try, do give it a go! The percentage pass mark for the overall test it was featured at in one of Scotland's higher Mathematics exams was lowered to 34% to compensate.

If you cannot figure it out, here is a YouTube video of a Maths fellow solving the equation.

[video=youtube]http://youtu.be/xko48OoTAQU[/video]

[CarnivorousJelly]

Dude that's a basic calculus question

... and by basic I mean I did several university courses that taught me how to do that over the last two years but I've since forgotten it. Okay maybe it's not so basic :p

I'm going to be a great engineer.

[CarnivorousJelly]

Double post but totally related to the problem you posted

[video=youtube]https://youtu.be/yBG8SSB763w[/video]

[Radiance]

Speaking of calculus, did you see parametrical formulas in SOMA? They are quite a few. For example
x(t)=a*(x-t) ...
I couldn't read them all because of small letters but are they representing the trajectory of ARK when launched and when orbiting in space ?