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?
This problem was edited to be solvable with one solution. However, there may be references in the discussion to my old answer (see edits) when there weren't the constraints 100 total employees or Contractor wage = $8500. We can now easily calculate the salaries from your information:
We also now have two other equations, labeling $A$, $B$, $C$ as the ...
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.
Since the keys are arranged in a circular fashion, I think I need to identify both an origin and a direction, no matter which way the key ring is rotated, and no matter how many keys are moved from one side to the other along the ring.
This should do it with minimum trouble:
You can always return the keyring to this position, and thereby identify each key.
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 ...
You should be able to tell the difference between a key which is
Then arrange them in a circular pattern from one key to the last like:
Need to know at the start which key works for each door and arrange them in this order on the ring.
It looks like
This works all nice and fine,
There may, of course, be something obvious I'm missing.
For the J:
With the L, there are some problems that are very similar to the Z case,
Here's the T:
And finally, the S:
And for completeness' sake, the solutions already found by others:
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 ...