DrKrettin

True - but it helps to know that there is a chess section and that the poster knows it as well.

No - K- A6 or B8

So the white pawn promotes to something black, and it's checkmate. But that is just a stupid interpretation of "any piece". Edit: I didn't see he had posted. I still think my half-move solution is better.

Of course it isn't. It's not even check.

I've found a solution for mate in HALF a move The pawn is about to take a piece on A8, which has already been removed from the board. It then becomes a queen - checkmate.

It looks impossible to me. I just can't see how to stop the king moving to B8, no matter what we assume. Even if it's a discovered check if the pawn moves to B6.....

I'm glad you said that. As far as I can see, the king can always move to B8 and not be in check, regardless of the direction the pawn can move in (which I suspect is a key to the problem)

Without having put much thought into it, is the symmetry you have discovered not independent of the base you are working in? So it's the same for octal or hexadecimal, or any base greater than 2.

On a different tack, if I may, the Guardian Word of the Year is Unpresidented My spellchecker here needs to be updated, because it is now a word. One meaning is unpresidentedAn instance of someone being “prepared to say what most of us are thinking”, but actually saying things most of us are not thinking Except, most of us are not thinking the things Trump is thinking. And if we are, it is only in the sense of: “Who in their right mind would think that?” The Guardian has an article here which gives some other definitions, such as An irrecoverable act of folly committed by a president

*sigh* What I said was in the context of your unnecessarily complicated solution of placing the seeds on the sphere so that they were equidistant from each other. I shall now take the trouble to expand what I said so that even you might understand: No matter how you place your seeds on the surface of that sphere such that they are all equidistant from each other, the 4 seeds will form the vertices of a regular tetrahedron. Happy now?

This is arguing a silly point to death. No matter how you place your seeds on the surface of that sphere, the 4 seeds will form the vertices of a regular tetrahedron. What else are you arguing about? You are using a sledgehammer to crack a nut.

Yes, too many variables. But if the rooms are adjacent and the the internal walls have no insulation value compared to the external walls, floors and ceilings of the apartment/house/castle/septic tank/cave, which is generally the case, I doubt whether it's going to make much difference.

No matter how you describe the process, the four seeds end up at the 4 corners of a regular tetrahedron. You can use the sphere to get there, but the answer has not changed.

What is wrong with the analogy of a hosepipe firing a jet of water at the moon? If the hosepipe were strong enough, any sideways movement would result in the end of the stream of water moving faster than light. Anybody who has ever used a hosepipe will know this is nonsense, the water just forms a curved trajectory.

Way too easy .....

This is really creepy. The amazing US of A chooses to elect an ignorant narcissist as president, and people think this is fine. Somebody who says he doesn't need intelligence briefings because he is smart. Let's just hope there really will be the opportunity for other elections, with this idiot in charge of nuclear weapons and the policy on global warming.

Considering that it has to be politicians who legislate to make this a crime, it isn't going to happen. Turkeys don't usually vote for Christmas (Thanksgiving?)

Such as grammar issues in the title?

It would be very difficult to answer the above in fewer than 100,000 words, and I'm too busy today.

I've done a rough calculation. See what you think. Let's draw an n-sided regular polygon where the perimeter is a constant P. We can divide the area into n symmetrical isoceles triangles where the base is P/n. The half angle at the centre is pi/n so the height h of the triangle is given by tan(pi/n) = P/2n.h. So the area of each triangle is P/2n. P/(2n.tan pi/n) So the total area is n times that, equal to P^2/(4n.tan(pi/n)) I'll leave it as an exercise for the student to show that that function increases with n to a limit of (pi.P^2)/4

You beat me to it. The greater the number of sides of a polygon, the greater the area (for a fixed perimeter). The circle is the case of an infinite number of sides.

So "Diel" is a word you have invented, which is fair enough. As for the Sabbath, you must mean Zeitgeber

The point is that there is a huge amount of indirect evidence for black holes, so there is good reason to suspect that they exist. This evidence puts black holes into a totally different category to "life after death" for which there is absolutely no evidence at all. The distinction is an important one.

I think it's changed its meaning since Old Norse. In Old Norse hundrath meant 120, that is the long hundred of six score, and at a later date, when both the six-score hundred and the five-score hundred were in use, the old or long hundred was styled hundrath tolf-roett ... meaning "duodecimal hundred," and the new or short hundred was called hundrath ti-rætt, meaning "decimal hundred."

Where does the name "diel" come from? and "It also suggests reasons for the great oxygenation event, the evolution of multicellularity, the Cambrian Explosion, and the Sabbath." I'm intrigued about the Sabbath. Please explain.