[soop]

Another chess question.

On a regular chessboard, what is the minimum number of knights you can place so that each knight (using its regular movement pattern) is in check by another knight.

[Guest]

Hi

It should be 14 knights......

7 for black and 7 for white....

7 nights can cover the whole chessboard of one color. 7*2(for white) = 14 total.....

What is the correct answer?????

Can you put that in a drawing using _ and X so we can see that? And remember that even though the 14 can cover a chessboard, 2 knights must be able to attack each positioned knight for them to be 'checkmated' and have no possible escape

[Guest]

Can you put that in a drawing using _ and X so we can see that? And remember that even though the 14 can cover a chessboard, 2 knights must be able to attack each positioned knight for them to be 'checkmated' and have no possible escape

I just read the thread again on page 1, where it is written that each knight is in check with another.

In that case, you are right.....28 is the correct answer then....

wat says the thread starter ?

[Guest]

I got 20.

0's are empty, 1's are knights:

00000000

00011000

00111100

01100110

01100110

00111100

00011000

No knight can take another knight without threatening themselves. No knight can even move to a corner space. All empty spaces are covered by 2 knights.

[Guest]

OK.... I'm sure this one has flaws too, but assuming that all knights can kill all other knights (no white or black), what about this layout

_ _ _ _ _ _ _ _

_ k k _ _ k k _

_ k _ k k _ k _

_ _ k k k k _ _

_ _ k k k k _ _

_ k _ k k _ k _

_ k k _ _ k k _

_ _ _ _ _ _ _ _

24 pieces (and full of flaws, I'm sure)

EDIT: corrected board typo

Edited August 28, 2008 by PoudreAvenger

[Guest]

I got 20.

0's are empty, 1's are knights:

00000000

00011000

00111100

01100110

01100110

00111100

00011000

No knight can take another knight without threatening themselves. No knight can even move to a corner space. All empty spaces are covered by 2 knights.

By the looks of things, the bolded ones could jump into the corners...

EDIT: Just noticed that there are only 7 rows, so I'm assuming there are more along the bottom to prevent the corner jumps

Edited August 28, 2008 by Mumbles140

[Guest]

What is the minimum number of knights you can place knights on a chessboard (using their regular movement pattern) so they fullfill the following critera:

1 - Each knight is in check from another night

2 - No knight cannot escape from check

This was my justification for believing that a knight still had to be in check after a jump, even if he 'conquered' another knight's square. Two knights cannot solely hold themselves in check for a given jump because one can eliminate the other, thus removing the threat of 'check' in that particular move. I haven't checked the others, but I'm assuming 28 is not the minimum because it was the first one I made fit using all 4 starting positions

[Guest]

EDIT: Just noticed that there are only 7 rows, so I'm assuming there are more along the bottom to prevent the corner jumps

Yeah, I just noticed I missed my bottom completely empty row.

The pattern is completely symmetrical. So it should be:

00000000

00011000

00111100

01100110

01100110

00111100

00011000

00000000

Now no one can get to the corners.

Edited August 28, 2008 by fish

[Guest]

But there are pieces that can jump to open spaces...In the 3rd row (from top or bottom), the exterior knights can jump 2 to the outside and 1 away from the middle to be on the row that is currently 00011000 That row will then become 10011001 with no way of reaching those end 1's, making them not in check

[Guest]

But there are pieces that can jump to open spaces...In the 3rd row (from top or bottom), the exterior knights can jump 2 to the outside and 1 away from the middle to be on the row that is currently 00011000 That row will then become 10011001 with no way of reaching those end 1's, making them not in check

I think it's a good layout. With what you're saying, the exterior knight in the 4th row has the knight you're talking about in check (one to the outside, two away)

Dang... 20... I don't think I can beat that.

[Guest]

My apologies--I seemed to have been counting better with _'s and X's than I was with numbers

[Guest]

But there are pieces that can jump to open spaces...In the 3rd row (from top or bottom), the exterior knights can jump 2 to the outside and 1 away from the middle to be on the row that is currently 00011000 That row will then become 10011001 with no way of reaching those end 1's, making them not in check

Every unoccupied space, except the corners, is threatened by any currently occupied space.

If 2's are the Knights you move, 3s are the ones that threaten them, and _ is their vacated spot The converse is true. If the 3s move to the 2 position, the _ threatens that spot.

00000000

20011002

00311300

0_1001_0

01100110

00111100

00011000

00000000

I created an 8x8 square in excel.

I labelled each of the knight positions k1-k20 (left to right, by row, top down) and then progressively went through the grid and marked the squares that each knight can move to. Every moveable square, has 2 possible knights that can move there, and every knight placed, has a knight that can take them from the start.

So using the Excel grid, for example, if the Knight in cell C3, moves to cell A2, the knight in B4 can take him. If the knight in cell C3 does not move, the knight in B5 will take him.

[Guest]

So how 'bout it soop? What's the minimum? If it's less than 20, just share the # so we can try and figure out the positions!

[Guest]

Yeah....I can't beat 20. I came up an alternate layout, but it still has 20.

[Guest]

What's your layout Poudre? I was somewhat wondering how a psuedo-inverse of mine would look, but figured it'd grow in scale since you're moving 'outward' from the ring.

[Guest]

What's your layout Poudre? I was somewhat wondering how a psuedo-inverse of mine would look, but figured it'd grow in scale since you're moving 'outward' from the ring.

Here's my other layout:

k _ _ _ _ _ _ k

_ _ k _ _ k _ _

_ k _ k k _ k _

_ _ k _ _ k _ _

_ _ k _ _ k _ _

_ k _ k k _ k _

_ _ k _ _ k _ _

k _ _ _ _ _ _ k

I'm pretty sure this works, but I've been wrong before.

[Guest]

I found another 20:

00000000

01011010

00011000

01100110

01100110

00011000

01011010

00000000

[Guest]

I'm not sure that one works... the knight in the second row, fourth column (counting from the top left) could move to the top row, second column, and be out of check.

[Prime]

Here is a set up for 17 knights, if they are not allowed capture.

[soop]

So how 'bout it soop? What's the minimum? If it's less than 20, just share the # so we can try and figure out the positions!

Hahah! TBH, I thought it would be at least half the squares on the board, but just reading through, I'm more and more astounded. I didn't thing Poudre's original 32 could be beater, but again and again, I've been proven wrong.

I just don't see how primes' epic configuration can be beaten.

Guys, just want to say I'm really stoked - I honestly didn't believe the puzzle would be this good when I thought of it (especially after the initial mistakes - grrr).

Thanks all

[Guest]

Hahah! TBH, I thought it would be at least half the squares on the board, but just reading through, I'm more and more astounded. I didn't thing Poudre's original 32 could be beater, but again and again, I've been proven wrong.

I just don't see how primes' epic configuration can be beaten.

Guys, just want to say I'm really stoked - I honestly didn't believe the puzzle would be this good when I thought of it (especially after the initial mistakes - grrr).

Thanks all

This has been a great puzzle, soop. If I haven't said it before, thanks for posting it!

[soop]

This has been a great puzzle, soop. If I haven't said it before, thanks for posting it!

you're welcome

[Guest]

I just don't see how primes' epic configuration can be beaten.

You can move to evade capture, by capturing in his, so I don't think his truly solves the problem.

[Guest]

10101010

00000000

01010101

00100010

10101010

00000000

01010101

00000000

oops...nevermind, i see a hole

Edited August 29, 2008 by KeithK

[soop]

You can move to evade capture, by capturing in his, so I don't think his truly solves the problem.

Ah, You're right, it's those odd two, isn't it. Always the way with these pesky knights.

Keith, every knight is in check, but they can evade

[Prime]

You can move to evade capture, by capturing in his, so I don't think his truly solves the problem.

OK then. If capture is allowed here is a nice symmetrical set up of 20:

A nice symmetrical arrangement:

Although, there is some ambiguity with respect to capture. If there are just 2 opposing sides -- black and white, like in chess, then after making a capture the knight is attacked only by its own color/side.