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Riddles guessing game!

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Original post by Laurasaur
A natural state, I'm sought by all. Go without me, and you shall fall. You do me when you spend, and use me when you eat to no end. What am I?


Balance is what I get from the first two sentences haha

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Did this earlier on a game, thought this was quite a really challenging maths problem to put in a children's game!
1453066851062.jpg

Posted from TSR Mobile
Original post by eternaforest
Did this earlier on a game, thought this was quite a really challenging maths problem to put in a children's game!
1453066851062.jpg

Posted from TSR Mobile


I'd have thought it was $50 each no matter how long it took each person because it says in the first paragraph that the plot of land was split in half.
Original post by TSRian123454321
I'd have thought it was $50 each no matter how long it took each person because it says in the first paragraph that the plot of land was split in half.


Hah that is the answer :biggrin: the rest is kinda supposed to throw you off.
Original post by eternaforest
Hah that is the answer :biggrin: the rest is kinda supposed to throw you off.


:woo:

Now to solve Laurasaur's riddle...
Original post by TSRian123454321
:woo:

Now to solve Laurasaur's riddle...

The first two sentences sound like it should be balance, but not sure what the rest of it means :s-smilie:
Original post by eternaforest
The first two sentences sound like it should be balance, but not sure what the rest of it means :s-smilie:


Well, it most likely has to be both an adjective or a noun, so balance makes sense...
I'm, afraid the original coins puzzle doesn't work. There is no angle you can view the coins and see a perfect rectangle, one edge will always be curved.
Ok my contribution.

An oldie but goodie.

There is a cup of black coffee and a cup of white milk. Equal volumes and sizes.

You take a teaspoon of the coffee and put it in the milk and stir it up. Assume it is now a uniform solution.

You then take a teaspoon of the Milk-coffee solution and put that into the black coffee cup and stir it up.

Question

Which cup now has the most of its original liquid?

Does the coffee cup have more coffee in it than the milk cup has milk? or vice versa?

Guesses are not permitted here as there are clearly only 3 possibilities.

Make your guess and provide the proof.
Original post by PilgrimOfTruth
I'm, afraid the original coins puzzle doesn't work. There is no angle you can view the coins and see a perfect rectangle, one edge will always be curved.


Or perhaps it does work based on the fact that rectangles are essentially two-dimensional and we three-dimensional beings are just ignoring a simple definition.
Original post by Wunderbarr
Or perhaps it does work based on the fact that rectangles are essentially two-dimensional and we three-dimensional beings are just ignoring a simple definition.


Nope. It simply doesn't work. Sorry.

You "imagine" a rectangle because your eyes are not sharp enough to perceive the tiny curvature of the top or bottom coin. Nevertheless, the shape seen is that of a barrel, straight edges on one side and curved edges on the other sides.

Even if you line yourself up perfectly on say the bottom plane of the bottom coin, then the top coin HAS to appear curved not straight.
Original post by PilgrimOfTruth
Nope. It simply doesn't work. Sorry.

You "imagine" a rectangle because your eyes are not sharp enough to perceive the tiny curvature of the top or bottom coin. Nevertheless, the shape seen is that of a barrel, straight edges on one side and curved edges on the other sides.

Even if you line yourself up perfectly on say the bottom plane of the bottom coin, then the top coin HAS to appear curved not straight.


The point is that it is supposed to be able to be passed off as a rectangle, being quite close to one from a certain point of view.
Let tt be the amount the teaspoon holds.

Coffee: cc, Milk: mm
Coffee: c+tmc + tm, Milk: m−tmm - tm
Coffee: c+tm−(t(c+tm))c+tm-(t(c+tm)), Milk: m−tm+(t(c+tm))m-tm+(t(c+tm))
Coffee: c+tm−tc−t2mc+tm-tc-t^2m, Milk: m−tm+tc+t2mm-tm+tc+t^2m

Coffee has c−tcc-tc coffee in it.
Milk has m−tm+t2mm-tm+t^2m milk in it.

If there are equal volumes of coffee and milk, then c=mc=m. Let's call the volume xx:

Coffee has x−txx-tx coffee in it.
Milk has x−tx+t2xx-tx+t^2x milk in it.
x−tx=x−tx+t2x[br]t2x=0[br]x-tx=x-tx+t^2x[br]t^2x=0[br]
So they cannot be equal.

x−tx>x−tx+t2x[br]t2x<0x-tx>x-tx+t^2x[br]t^2x<0
Which is impossible since t,x>0t, x > 0.

Therefore the milk has more milk than the coffee has coffee! (I think...)
Original post by Wunderbarr
The point is that it is supposed to be able to be passed off as a rectangle, being quite close to one from a certain point of view.


"passed off", "quite close" are not terms generally expected in brainteasers and riddles TBH. If people are expected to expend time and effort to work out a solution, that solution needs to be true.
Original post by otah007
Let tt be the amount the teaspoon holds.

Coffee: cc, Milk: mm
Coffee: c+tmc + tm, Milk: m−tmm - tm
Coffee: c+tm−(t(c+tm))c+tm-(t(c+tm)), Milk: m−tm+(t(c+tm))m-tm+(t(c+tm))
Coffee: c+tm−tc−t2mc+tm-tc-t^2m, Milk: m−tm+tc+t2mm-tm+tc+t^2m

Coffee has c−tcc-tc coffee in it.
Milk has m−tm+t2mm-tm+t^2m milk in it.

If there are equal volumes of coffee and milk, then c=mc=m. Let's call the volume xx:

Coffee has x−txx-tx coffee in it.
Milk has x−tx+t2xx-tx+t^2x milk in it.
x−tx=x−tx+t2x[br]t2x=0[br]x-tx=x-tx+t^2x[br]t^2x=0[br]
So they cannot be equal.

x−tx>x−tx+t2x[br]t2x<0x-tx>x-tx+t^2x[br]t^2x<0
Which is impossible since t,x>0t, x > 0.

Therefore the milk has more milk than the coffee has coffee! (I think...)


Beautifully laid out explanation.

But wrong . . . sorry :-(
Original post by PilgrimOfTruth
I'm, afraid the original coins puzzle doesn't work. There is no angle you can view the coins and see a perfect rectangle, one edge will always be curved.


You're really bringing perspective into this? Just because it appears curved, it doesn't mean it is curved.

Regardless, we're talking about making a 2 dimensional plane using 3 dimensional objects - and taking any cross-section of the stacked coins in that direction will provide you with a rectangle. :cute:
Original post by Alexion
You're really bringing perspective into this? Just because it appears curved, it doesn't mean it is curved.


I'm desperately trying not to be a pedant on this but I know I'm right.

This boils down to a simple curved line.

You can rotate ONE curved line in 3d space and when you view "on plane" as it were that curve then appears as a straight line.

That's fine.

As soon as you introduce another curved line into the situation, and specifically one that is parallel to the other then the 2nd curve will NEVER appear straight.
No matter where you view from only one of the curved lines will appear as a straight line.
Original post by PilgrimOfTruth
x


By your logic, no object can have straight sides.

If you use perspective as an argument, then the side of my computer (which I know is a square) isn't a square.

It's either this:



... or this:



... when I know it's most definitely this:

If your PC "box" is made up of straight lines then no matter what angle you view it from, those lines will ALWAYS appear as straight lines. Perspective may make a line look longer or shorter and may make a line look tilted, but it will never make a straight line look like a curved line.

A straight line, viewed from any angle, is always a straight line.

A curve on the other hand is different. A curve will ALWAYS appear as a curve EXCEPT when viewed anywhere directly level with the plane of the curve. When you view on the plane, the curve appears as a straight line. So look at the rim of your coffee cup and it's always a curve unless you look at it directly level.
But when you look at the top of that cup directly level, then look at the bottom of the cup and you have to see and understand that the bottom must look curved because your sight line is still level with the top of the cup.

With your PC front, there is only ONE position you can view it and actually see a perfect rectangle and that's when viewing it dead centre. Move up or down and as your diagrams suggested, the rectangle becomes some kind of trapezoid.

This is useful discussion TBH. If you were to take up art and try to draw a tall glass you'd quickly see that it looked completely wrong if the side view was painted as a rectangle :-)
@Otah007

Are you going to have another go at the coffee-milk conundrum?

Here's a clue, and a useful way to solve any problems such as this one. If a problem, in its asking, does not state specific volumes or measurements, then by definition, the solution must work for ANY volume or measurement. That being the case, you can use whatever volumes you wish, so use volumes that are useful. You can deduce the answer without any maths at all if you choose the right volume.

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