Is there a mate?

Logic Level 3

It’s white turn to move. If white and black play optimally, what is the minimum number of moves for white to checkmate the black king? If in your opinion, mate cannot occur, input your answer as 0 0 .

2 4 0 8 3 9 1 5

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1 solution

The first move for white is Rh6! \text {Rh6!} . Minimum number of moves is 9 9 . Here is the solution of the puzzle from my source.

1. R h 6 + R h 7 1.Rh6+ Rh7

2. R x h 7 + K x h 7 2.Rxh7+ Kxh7

3. Q f 7 + K h 8 3.Qf7+ Kh8

4. Q e 8 + K h 7 4.Qe8+ Kh7

5. g 6 + K h 6 5.g6+ Kh6

6. B f 4 + K h 5 6. Bf4+ Kh5

7. g 7 + K g 4 7.g7+ Kg4

8. g 8 = Q + K h 4 8.g8=Q+ Kh4

9. 9. B g 3 Bg3 # \#

Why start with Rh6 ? How do you know the answer cannot be less than 9?

Pi Han Goh - 4 years, 1 month ago

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It needs deep calculation. It takes time because we need to consider some variations.

A Former Brilliant Member - 4 years, 1 month ago

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What deep calculation? This is a chess puzzle, why would there be any "deep calculation" involved?

What variations are you referring to?

Pi Han Goh - 4 years, 1 month ago

Rh6 \text{Rh6} is the first move of the solution from my source.

A Former Brilliant Member - 4 years, 1 month ago

I gave this some thought, but couldn't come up with a forcing sequence, with all checks.

I was convinced it was more than 3 moves, likely much more.

I could see some strong threats that would lead to a certain checkmate, but I convinced myself that the black Queen could deliver perpetual checks if given the chance.

I'd like to see the whole solution, but if it's got too many variations it seems like a computer solution would be the only reasonable path to certainty.

Steven Perkins - 4 years, 1 month ago

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I posted the solution of the puzzle. I checked with my computer engine and found out that there are variants but it will end all in mate in 9 moves.

A Former Brilliant Member - 4 years, 1 month ago

Thanks for posting this solution. I hadn't thought to choose 4. Qe8+ allowing the pawn to advance and covering the white squares.

A main variant seems to be in response to move 4, where black might reply 4. ...Kg7. I'm trying to calculate where that might take the game, but haven't yet envisioned a solution.

Not an easy problem for a human, at least for me. I think it should be rated a level 4 or 5.

Steven Perkins - 4 years ago

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