How to fill in all spaces on a 7x7 board

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SolaireLight
Posts: 5
Joined: 19 August 2023, 14:43

How to fill in all spaces on a 7x7 board

Post by SolaireLight »

Is there some trick to laying the tiles or things you avoid to make sure that you can fill in the entire 7x7? I'm saying making sure that all of your tiles fit on the board. It's trivial to make them all fit in a 5x5, but in 7x7 it feels like it is much more difficult.
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Mathew5000
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Joined: 02 January 2021, 01:41

Re: How to fill in all spaces on a 7x7 board

Post by Mathew5000 »

SolaireLight wrote: 08 January 2024, 04:53 Is there some trick to laying the tiles or things you avoid to make sure that you can fill in the entire 7x7? I'm saying making sure that all of your tiles fit on the board. It's trivial to make them all fit in a 5x5, but in 7x7 it feels like it is much more difficult.
Yes, there are a few tricks. The main thing is, whenever you place a domino touching an edge of the grid, first check to see if this is going to create two separate regions of empty space. If so, it's crucial that each region has an even number of squares. That is a necessary condition but not sufficient. Don't place a domino so as to isolate a 3x3 region. There are also some jagged shapes which, even though they contain an even number of squares, cannot be filled by dominos. The best thing is, before you place any domino, just imagine where on your board you might place the next few dominos.
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SolaireLight
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Joined: 19 August 2023, 14:43

Re: How to fill in all spaces on a 7x7 board

Post by SolaireLight »

Those tips make sooo much sense! The placement for the edge of the board helps a lot. I'll give them a try and let you know how it goes!
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