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Knights on a chess board

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What is the maximum number of knights you can place on a regular chess board, so that each square has at most one knight threatening or occupying it?

What is the minimum number of knights you can place on a regular chess board, so that each square has at least one knight threatening or occupying it?

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Posted (edited) · Report post

I can do it with 16 knights. I'm sure that's not the minimum, but it's a start. 4 squares of 4 with the knights in front of the 2nd and 3rd pawns.

Edited by Rob_Gandy
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Posted · Report post

That's a good start, but it's not the minimum.

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Posted · Report post

14

--------

--K--K--

--KKKK--

--------

--K--K--

-KK--KK-

--K--K--

--------

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Posted · Report post

12

--------

--K-----

--KK-KK-

-----K--

--K-----

-KK-KK--

-----K--

--------

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Posted (edited) · Report post

Nice improvement, keep going ;)

Edit: scratch that, looks like you found the minimum :)

Edited by Rainman
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Posted · Report post

I can do 12.

k-----kk

kk----k-

--------

--------

--------

--------

-k----kk

kk-----k

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Posted · Report post

And that's the maximum, well done!

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Posted · Report post

12

--------

--K-----

--KK-KK-

-----K--

--K-----

-KK-KK--

-----K--

--------

I can do 12.

k-----kk

kk----k-

--------

--------

--------

--------

-k----kk

kk-----k

In both the maximum and minimum the knights are placed in the same basic pattern. That and they are the same number...

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