As far as I know, the only way to figure this out is by letting a computer run through all the possibilities. It is a small puzzle, so this does not take long.
First I will assume that you want the final solved position to have the blank in the bottom right corner, with the tiles in numerical order:
(See further below for the results with the ...
Here are my first idea (both sides are essentially the same answer, so the hint fits too):
Both positions seem to be independently reachable by a legal game. It might be possible to find a legal game leading to the whole position too, but that would take a bit of time.
Before that, I'm going to double check for any simpler solutions. :-)
Since OP ...
My position has a fourteenth check too, but that's probably ok. :-)
These are the moves:
And here's the whole solution uploaded to Lichess.
EDIT: Looks like 15 is also doable:
The final check feels like such a waste of a piece though; the first fourteen checks are possible with white having only two pieces and a king:
Again, here's the Lichess link.
I must be missing something because I'm getting a lot more than 54 mates-in-two for the position below? I have 116 listed, although I'm doing this by hand so there may be some errors included. Is there some rule I haven't considered?
EDIT: A winning knight underpromotion I found. All other promotions lead to wins, but underpromoting to a knight is the fastest mate (mate in 1).
EDIT: Thanks to RosieF for catching a huge error in the bishop part.
I haven't seen this puzzle before. I cannot tell you the name or who produced it.
But assuming your goal is to reassemble it, I can help.
It seems the problem is to fit all 5 pieces in a 4x4x4 cube. In the solution there are visible holes left.
Edit: As Weather Vane noted, a missing 6th piece can complete the puzzle. The goal was to build a solid ...
Following the excellent answer from @FlorianF here is a set of images showing his missing piece (four angles). This is Florian's solution, not mine, I just added a graphic.
I have not seen this exact puzzle. I wondered if it is complete.
So I am as mystified as ever by the puzzle, but perhaps the centre must be filled too.
Here is the answer for practice ones:
To construct b=3;
As show below for i=9.
The general idea is actually the same as above, if you want to increase b
for example, if you want b=5 and i=9;
or for example, if you want b=20 and i=9;
So you should
so you can create polygons with every $i\geq0$ and $b\geq3$ values with the method above.
Here's a situation where promoting to queen is the only winning move:
1 h8=Q! wins
1 h8=R? only draws:
Here's a situation where promoting to bishop is best:
Promoting to bishop
Promoting to queen
Promoting to knight
Promoting to rook
As luck would have it, this morning, YouTube recommended to me a video discussing a win-study by Selezniev which ...
OK, so here's my track design, or at least the functional part of it.
I call it The Candle of Chicken.
Unlike the examples above, I've marked the spots that are not walls, that is, there's only a very narrow path available from the start at the bottom.
The starting points are symmetrical, and there's only one choice to make: Either stop after the first ...
I drew it!
Everything below is my original post:
@Bass had a very similar idea to mine. Funny how that works. I was going to wait and try to actually draw it, but I feel like it isn't worth the effort, now.