harey

Wording made some of the rules sort of shaky.

Now, I have a problem. witzar was the first to answer and his answer is correct. ThunderCloud answered 1 minute later and his explication is clearer. Can I attribute two Best Answers? Anyway, congratulations to both that they did not fell into the trap.

Let's toss a fair coin and note the events. When H H H appears, I pay three bucks When T H H appears, you pay one buck. And then we start over. Who is willing to play?

Yes, I see. There must be a lot of solutions, like taking a sphere and a cube and drilling holes into the cube until it becames lighter than the sphere - no formula, no misscalculation. My preferred solution is still that of the three squares and three pankaces in the planes xy, xz and yz. BTW, the Volume=3a2d-d3 - I have the same oversight in my post n. 8. I just wonder how often we make false deductions in the real life in the style "three projections=circle => it must be a sphere".

The best way is to make them of equal volume ( suppose what I call a "3D square" is a prism?): v_prism=a*a*d_prism v_cylinder=pi*a/2*a/2*d_cylinder => d_cylinder=(4/pi)*d_prism While it might work for small d, with growing d, it will became more and more perceptible that the cylinder should be a kind of barrel (or a pancake). The formulae get too complicated for my taste and my possibilities.

The circle is inscribed to the square... That's easy. The circle is inscribed to the square.

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I think it is a pity that the solution is not posted when nobody finds it. So here we go:

I do not accept. .

Prayer to bona alma: - correct the post 4 with the correction from the post 5 - delete in the post 4 remarks that are not necessary anymore - delete the post 5 - delete this post ...and pray with me that bmad concedes it is the Best Answer

Correction: B sends: - if(measurement<4) measurement else 7-measurement. P.S. It would not be bad if the table in my previous post magically appeared in a fixed font.

Sorry I cannot hide it. Maybe because of the font? Edit: Definitely, I have a problem with the editor.

Reasoning from a similar problem:

@Grimbal You can continue: - there are 50.5 boys born per 49.5 girls. - women live longer.

Really easy!!! And even more. No one said that the 401 circles may not have a smaller diameter. No one said that they may not ovelap.

We know that A sees B=334 and c=334 - A CANNOT see B=335 and C=334. (Not to confound with: "As this information in not available to him, he ASSUMES he has 334 or 335.") So my first answer was correct. In the 2nd try, I got lost and could not correct quickly enough.

I know a better and harder version, if I find it, I'll post it. Does it matter if it is in French?

Myself, I would prove it for N=0 and leave the proof for N>0 to the reader If you try for some N, you quickly see the law.