Genady

Yes, this is a crucial condition:

I did: and the response was: Fail.

But computers are electronic rather than mechanical devices.

I wonder how this experience fits into the idea of tapping into a collective unconscious.

I don't think it is new. I also think that it is pointless.

If the mirrors were convex it would show in this picture:

Yes, it is developing in a fast pace, but IMHO the direction of this development is tangential to the evolution we are discussing here. It goes in the direction of efficient emulation of human activities, but there is nothing yet to suggest an emergence of independent intelligence.

Neutrons don't have electric charge. They are not affected by electromagnet.

You can change the mass by attaching to the moving body "on the fly" two other bodies of equal mass coming to it from two sides with equal speed and moving with the same speed in the same direction as the central body. Can you rephrase you question for this scenario?

Some clarifications required: 1. If it is pushed, before the mass change, it is not moving with a constant speed, but rather accelerates. 2. What is "kinetic force"? I am familiar with "force" and with "kinetic energy", but not with "kinetic force". 3. What "antigravity" has to do with mass change?

Sorry, you are right. I didn't notice the minus sign in this image: My apologies. The final expression in the OP was incorrect, but you have corrected it.

Perhaps, the pictures here, Giant Sun Mirrors of Rjukan – Rjukan, Norway - Atlas Obscura, give the idea. The mirrors are flat, and the light spot is not big. More story and pictures here: The dark town that built a giant mirror to deflect the Sun - BBC Future.

IOW, thinking Absolutely! Agree 100%. Me too. Maybe a bit earlier. Been a member of Baku youth astronomy club between about 9 and 14 yo. Wonderful lifelong memories.

No, these two expressions above certainly do not equal each other. I can prove it. Moreover, the second expression cannot be a probability at all.

Some clarifications here: optics - Is light dispersed over distance by flat mirrors? - Physics Stack Exchange

I know. I mean, the formula as it appears here https://www.scienceforums.net/topic/131457-computing-the-probability-of-voting-of-the-member-of-parliament/?do=findComment&comment=1238311 is incorrect.

What is "eclipse shape of mirror"? In the article, the mirrors appear to be flat.

Still incorrect.

I don't think it is correct. Check the algebra.

Hmm... I don't know regarding coding. I've just written a little program today (https://www.scienceforums.net/topic/131412-puzzle-for-the-day/?do=findComment&comment=1238294) after more than 20 years break. It felt like I never stopped.

As an alternative to Sensei's C/C++ code above, here is an Excel VBA code. Not polished and without an attempt for optimization but uses recursion. Runs quite fast, too. Stops at the first answer. Dim itry(1 To 10) Sub main() puzzle0 1 End Sub Sub puzzle0(k) For l = 0 To 9 itry(k) = l For i = 1 To k - 1 If itry(i) = itry(k) Then GoTo line1 Next i If k < 10 Then puzzle0 k + 1 Else x = itry(1) * 10000 + itry(2) * 1000 + itry(3) * 100 + itry(4) * 10 + itry(5) y = itry(1) * 10000 + itry(6) * 1000 + itry(7) * 100 + itry(1) * 10 + itry(8) v = itry(9) * 100000 + itry(7) * 10000 + itry(1) * 1000 + itry(7) * 100 + itry(6) * 10 + itry(10) If v = x + y Then Cells(13, 5) = x Cells(14, 5) = y Cells(15, 5) = v GoTo line0 End If End If line1: Next l line0: End Sub

Thank you for your reply. Unfortunately, there is a mistake in your calculations: 17 apples with the weights you suggest go up to x17 = 233 rather than 231. Thus, their total weight is 3689. Let's remove x2 now. The total weight of the remaining 16 apples is 3486. Half of it is 1743. As this is an odd number, there is no way to get it by any combination of 8 of the remaining apples. Thus, the puzzle is not solved, and I have nothing to inform my farmer friend. BTW, this is a mathematical puzzle, and they could be snails instead of apples as well. We can use any convenient real numbers. 1 to 33 are easier to deal with than 201 to 233, with the same result.

Right. There should be an even number of answers because for each answer the Y and H can be interchanged as they don't appear anywhere else. +1

These are good examples. +1

It says, that the entire universe is at least 1023 bigger than the observable universe.