Constructing the longest chain of identically notated…
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Constructing the longest chain of identically notated moves
I quite like when the move notation is the same for two or more moves in a row. Sometimes in a game you get `exd5 exd5`, or even `Rxc8 Rxc8 Rxc8 Rxc8`. That's fun.
I wonder how long it's possible to go on making identically notated moves. Can we construct a reachable position which allows the longest possible chain of legal moves with identical notation?
For this exercise, I will consider that checks, mates, and captures are **distinct** moves from each other, since their notation is not identical: Qa1, Qxa1, Qa1+, and Qa1# are all different moves.
My first thought was something like this:
https://i.ibb.co/FkCBd0cw/image.png
There are 9 queens per side, which is the maximum possible under normal rules assuming 8 promoted pawns. Each queen can take on e4 in sequence. But immediately there's a problem: piece disambiguation. The first move might be Qdxe4, followed by perhaps Qfxe4. Since multiple queens could take e4, the notation has to disambiguate which piece is being moved. Boo. No good.
So, since I'm only counting moves if the notation is **exactly the same**, this reveals that disambiguated moves are also distinct: Qaxa1, Q1xa1, and Qc3xa1 are all different moves.
However, in playing around with this idea I noticed that the queens on g2 and h7 are pinned, so can't legally move until the opponent first moves the g6/h1 queens. That will turn out to be useful to allow notationless disambiguation.
With a bit more thought, I came up with this new approach of interleaving opposite coloured queens in a line:
https://i.ibb.co/ZpGp5Qnc/image.png
I'm using fewer queens now, but the idea is that each queen only sees a8 once the queen ahead moves. Therefore `Qxa8+ Qxa8+ Qxa8+ Qxa8+ Qxa8+ Qxa8+ Qxa8+` is an unambiguous chain of 7. Progress!
Using the pin idea, I was able to expand this a little by pinning one more queen per side using the last queen in the chain:
https://i.ibb.co/4wVjRxXM/image.png
Now `Qxb7 Qxb7 Qxb7 Qxb7 Qxb7 Qxb7 Qxb7 Qxb7` is unambiguous. A chain of 8! Cool. >!However placing an extra pawn to block the check between b2 and h8 is unavoidable.!<
Developing that idea, I wanted to use the last queen in the chain to pin the first queen in a second chain, so that only once the first chain completes can the second chain be unleashed. This lead me to this position:
https://i.ibb.co/35Cj7ts1/image.png
Here, `Qxa5 Qxa5 Qxa5 Qxa5 Qxa5 Qxa5 Qxa5 Qxa5 Qxa5 Qxa5` is unambiguous. A chain of 10! :D
Note that it's important that both kings are legally placed and not in check. Annoyingly, I can't complete the second chain by adding a black queen on h5 since it would check the white king on e8.
Finally, the simple and fairly obvious-in-retrospect idea of just queueing up a load of queens in two conga lines seems to do best:
https://i.ibb.co/WpDpj5b9/image.png
This leads to a chain of length 12: `Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1`.
With only queens, there's nowhere for a 7th queen of either colour since there would be nowhere to place the king. Unless we add a single pawn, in which case..
https://i.ibb.co/TM5kZ60x/image.png
`Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1`. A chain of 14. Just look at it. Isn't it beautiful? I think we have a winner.
Here the queens could instead be rooks, but that would involve a lot of underpromotion!
I've been playing around with the analysis board and I haven't been able to beat my high score of 14. Can you make a longer chain? Even better, it'd be cool to see a **proof** which shows what the maximum length can possibly be. I suspect 14 can't be beaten.
#games
source
I quite like when the move notation is the same for two or more moves in a row. Sometimes in a game you get `exd5 exd5`, or even `Rxc8 Rxc8 Rxc8 Rxc8`. That's fun.
I wonder how long it's possible to go on making identically notated moves. Can we construct a reachable position which allows the longest possible chain of legal moves with identical notation?
For this exercise, I will consider that checks, mates, and captures are **distinct** moves from each other, since their notation is not identical: Qa1, Qxa1, Qa1+, and Qa1# are all different moves.
My first thought was something like this:
https://i.ibb.co/FkCBd0cw/image.png
There are 9 queens per side, which is the maximum possible under normal rules assuming 8 promoted pawns. Each queen can take on e4 in sequence. But immediately there's a problem: piece disambiguation. The first move might be Qdxe4, followed by perhaps Qfxe4. Since multiple queens could take e4, the notation has to disambiguate which piece is being moved. Boo. No good.
So, since I'm only counting moves if the notation is **exactly the same**, this reveals that disambiguated moves are also distinct: Qaxa1, Q1xa1, and Qc3xa1 are all different moves.
However, in playing around with this idea I noticed that the queens on g2 and h7 are pinned, so can't legally move until the opponent first moves the g6/h1 queens. That will turn out to be useful to allow notationless disambiguation.
With a bit more thought, I came up with this new approach of interleaving opposite coloured queens in a line:
https://i.ibb.co/ZpGp5Qnc/image.png
I'm using fewer queens now, but the idea is that each queen only sees a8 once the queen ahead moves. Therefore `Qxa8+ Qxa8+ Qxa8+ Qxa8+ Qxa8+ Qxa8+ Qxa8+` is an unambiguous chain of 7. Progress!
Using the pin idea, I was able to expand this a little by pinning one more queen per side using the last queen in the chain:
https://i.ibb.co/4wVjRxXM/image.png
Now `Qxb7 Qxb7 Qxb7 Qxb7 Qxb7 Qxb7 Qxb7 Qxb7` is unambiguous. A chain of 8! Cool. >!However placing an extra pawn to block the check between b2 and h8 is unavoidable.!<
Developing that idea, I wanted to use the last queen in the chain to pin the first queen in a second chain, so that only once the first chain completes can the second chain be unleashed. This lead me to this position:
https://i.ibb.co/35Cj7ts1/image.png
Here, `Qxa5 Qxa5 Qxa5 Qxa5 Qxa5 Qxa5 Qxa5 Qxa5 Qxa5 Qxa5` is unambiguous. A chain of 10! :D
Note that it's important that both kings are legally placed and not in check. Annoyingly, I can't complete the second chain by adding a black queen on h5 since it would check the white king on e8.
Finally, the simple and fairly obvious-in-retrospect idea of just queueing up a load of queens in two conga lines seems to do best:
https://i.ibb.co/WpDpj5b9/image.png
This leads to a chain of length 12: `Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1`.
With only queens, there's nowhere for a 7th queen of either colour since there would be nowhere to place the king. Unless we add a single pawn, in which case..
https://i.ibb.co/TM5kZ60x/image.png
`Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1 Qxa1`. A chain of 14. Just look at it. Isn't it beautiful? I think we have a winner.
Here the queens could instead be rooks, but that would involve a lot of underpromotion!
I've been playing around with the analysis board and I haven't been able to beat my high score of 14. Can you make a longer chain? Even better, it'd be cool to see a **proof** which shows what the maximum length can possibly be. I suspect 14 can't be beaten.
#games
source
| 1,000 mlx | |
| 3 | |
| 0 |