Post whacky or neat math stuff

[Addled Platypus]

get a chess board

place a penny on the first square

doulbe the amount on the next (i.e. 2)

and keep on doubling on each square there after (4,8,16)

how many pennies would there be on the last square....

[BeBMan]

I thought this is an old (Indian?) story, with rice corns instead of pennies. At least that we were told by out math teacher in school who said we should calculate as much numbers for those fields as we could within the 45 mins. math "hour"

[Ecthy]

1st square: 2^0
2nd square: 2^1
..
64th square: 2^63

All squares together: 2^64-1

[Harovan]

An oldie but goodie...

There's a cylindrical well with some amount of water in it. 2 sticks stand in it, reaching from the bottom at one side to the wall on the other and crossing themselves exactly at the surface of the water. One stick is 3 meters tall (or any other unit), the other 2 meters. The water stands 1 meter high. What's the diameter of the well?

[Ecthy]

2 meter to the width as the short bit above the water to the bit of water left to it (beams). Can't be arsed to do the math now but I think I'd use this approach.

Edit: you'd probably end up with one variable too many and then use the 3m beam to clarify things.

[Harovan]

It's a draft without scale, just to show how the sticks stand.

[Ecthy]

Scale is irrelevant if we have units. The corners are 90° I suppose and the water edge is parallel to the ground?

[Harovan]

What part of "cylindrical" did you not understand? And yes, it is perpendicular.

[Ecthy]

The way you put the problem it is pretty much reduced to 2 dimensions.

[Harovan]

Sure it's 2-dimensional, all takes place on a diametral cut through the 2 sticks. This doesn't mean it's as easy as it looks, though.

[Dauphin]

1.233 units.

Pot luck.

[Harovan]

IIRC that's a good approximation. I made an exact solution (no graphics, no iterations) with 6 digits in the 80's and wrote it down in a notebook, which I hope I can find when I'm at home. If memory serves right, it starts with 1.231...

How did you find it, graphical?

[Ecthy]

Originally posted by Sir Ralph
Sure it's 2-dimensional, all takes place on a diametral cut through the 2 sticks. This doesn't mean it's as easy as it looks, though.

The complexity of the problem has nothing to do with any cylinders anyway, rather with the fact that the width of the system is pretty basical to it.

[Harovan]

The remark "What part of "cylindrical" did you not understand?" was more directed at your question about the 90° corners.

[Ecthy]

Stop confusing people. Now why is this not as straightforward as it is supposed to be?