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        riddles >> easy >> Checkers
        
(Message started by: ThudanBlunder on May 11^th, 2008, 3:19am)

Title: Checkers
Post by ThudanBlunder on May 11^th, 2008, 3:19am

Here are a few checkers problems.
The rules are as in US and UK: 8x8 board, only kings can move backwards one square, and of course capturing is compulsory.

1) I once won a small bet against a local checkers player who was not as good as he thought he was (although he was better than me). "I could give you a man start and you still couldn't beat me," I hustled. "Oh yeah?" growled the mark. "Yeah. OK, I'll give you two kings to my one, I'll set 'em up and you go first, OK?" I said. He accepted and lost. How?

2) In the position below, it is Red (moving down the board) to move. Is it possible for him to crown the next man he moves?

Title: Re: Checkers
Post by mikedagr8 on May 11^th, 2008, 5:29am

For 2, if I understood the question correctly (which I assume I didn't) if red moves the piece on 19 to 24, it must reach the end of the board and be kinged.

Title: Re: Checkers
Post by ThudanBlunder on May 11^th, 2008, 8:25am

on 05/11/08 at 05:29:26, mikedagr8 wrote:

For 2, if I understood the question correctly (which I assume I didn't) if red moves the piece on 19 to 24, it must reach the end of the board and be kinged.

Yes Mike, it looks like you understood the question correctly.
Unfortunately, it doesn't seem to have helped you get the right answer. :P

Title: Re: Checkers
Post by temporary on May 11^th, 2008, 9:38am

Red can clearly king the piece to the right, but he has lost the game. In checkers, the one who has more pieces wins unless the position is bad for one side and makes them lose a piece. I was told checkers is binary, but does anyone know how?

Title: Re: Checkers
Post by ThudanBlunder on May 11^th, 2008, 11:51am

on 05/11/08 at 09:38:43, temporary wrote:

Red can clearly king the piece to the right, but he has lost the game. In checkers, the one who has more pieces wins unless the position is bad for one side and makes them lose a piece.

So you are an expert in checkers as well, are you? We are so lucky to have such a smart fella onboard.
The bigger army wins unless they have screwed up? Now we know. You must have been reading Sun Tzu.

As for the puzzle, you are wrong.

Yes, checkers is 'binary' in that one side moves first and the other side moves second.
I think you should stick to Rock, Paper, Scissors.

Title: Re: Checkers
Post by temporary on May 11^th, 2008, 12:17pm

Thanks, I think. This puzzle is easy, because it is in easy. I know that you are the janitor of the hard puzzles, so yes your puzzle is also somewhat hard. Red loses and doesn't get a king if it is white's turn, but gets the king and still loses if it's red's turn. I still don't quite get how the order of turns makes it binary, but that is a very helpful hint.

Title: Re: Checkers
Post by ThudanBlunder on May 11^th, 2008, 12:25pm

on 05/11/08 at 12:17:11, temporary wrote:

Red loses and doesn't get a king if it is white's turn, but gets the king and still loses if it's red's turn. I still don't quite get how the order of turns makes it binary, but that is a very helpful hint.

It doesn't matter who loses.
I asked if Red can crown the next man he moves.
You say yes, I say no.

I don't know what you mean by checkers being 'binary'.

Title: Re: Checkers
Post by ThudanBlunder on May 11^th, 2008, 12:42pm

on 05/11/08 at 12:41:03, Hippo wrote:

1. ... 25
2. ..? 24
3. ..?

Title: Re: Checkers
Post by Hippo on May 11^th, 2008, 12:43pm

1) It seems to me I don't understand the rules ... King ... one step backwards? I don't want to google them now...

2)
1. ... 25
2. ?x? 24
3. ..? 28
4. ..? 32

Sorry ... the update was too slow ... :)

Title: Re: Checkers
Post by ThudanBlunder on May 11^th, 2008, 12:49pm

on 05/11/08 at 12:43:33, Hippo wrote:

1) It seems to me I don't understand the rules ... King ... one step backwards? I don't want to google them now...

1) A king moves the same as an ordinary man, except it can also move backwards.
In some versions of checkers a king can move almost like a bishop in chess. But not here.

2) Sorry I don't understand your notation.
eg. moving from 31 to 27 would be denoted by 31-27
By the way, Red moves first.

Title: Re: Checkers
Post by temporary on May 11^th, 2008, 3:42pm

on 05/11/08 at 12:25:54, ThudanBlunder wrote:

I asked if Red can crown the next man he moves.
You say yes, I say no.

No?! What logic gate are you using? Red kings the one to the right by moving to the lower right then the lower left of that(white's move doesn't matter).

Title: Re: Checkers
Post by ThudanBlunder on May 11^th, 2008, 4:15pm

on 05/11/08 at 15:42:30, temporary wrote:

No?! What logic gate are you using? Red kings the one to the right by moving to the lower right then the lower left of that(white's move doesn't matter).

I post puzzles like these in the hope that people like you will come along and make them look good.
Thanks for being so predictably obliging.

Title: Re: Checkers
Post by Obob on May 11^th, 2008, 7:21pm

Hint: if somebody can capture a piece, they HAVE to. [hide]This includes if a king can capture a piece by moving backwards.[/hide]

Title: Re: Checkers
Post by temporary on May 11^th, 2008, 8:27pm

I know that. That is why starting with a king instead of a normal piece doesn't affect the game at all.

Title: Re: Checkers
Post by Sealock on May 11^th, 2008, 10:13pm

If red's first move is 19-24, what strategy by white can prevent the piece beginning at square 19 from being kinged? (In other words, please demonstrate why the first response you received in this thread is incorrect, because at first glance it is very difficult to believe.)

Title: Re: Checkers
Post by mikedagr8 on May 12^th, 2008, 3:23am

on 05/11/08 at 22:13:51, Sealock wrote:

Thanks now I seem to have understood.
The piece on 30 will have to be taken if played correctly; so the the piece on 19 will not get the opportunity to king.
If red moves 19-24 then white can simply move 30-25, and it must be taken. Hence red will not have moved its first piece and have it being kinged before the other.
Let's hope I understood more now and had a correct answer. :P

Title: Re: Checkers
Post by towr on May 12^th, 2008, 3:32am

So the answer to 2 is simply no?
If 21 moves, white takes it; if 19 moves, white can force 21 to move and be kinged first

Title: Re: Checkers
Post by ThudanBlunder on May 12^th, 2008, 3:40am

on 05/12/08 at 03:32:06, towr wrote:

So the answer to 2 is simply no?
If 21 moves, white takes it; if 19 moves, white can force 21 to move and be kinged first

The question didn't say anything about crowning 'first'.
It boils down to 'If Red plays 19-24 can he crown that man?'

on 05/11/08 at 22:13:51, Sealock wrote:

All in good time. :P

Title: Re: Checkers
Post by mikedagr8 on May 12^th, 2008, 4:10am

If we assume red does move 19-23 I have found a way so that he doesn't. Still working on a way for 19-24.

Title: Re: Checkers
Post by ThudanBlunder on May 12^th, 2008, 4:13am

on 05/12/08 at 04:10:31, mikedagr8 wrote:

If we assume red does move 19-23 I have found a way so that he doesn't. Do we assumse red does move 19-24?

Yes, we can assume Red is trying to crown and is not on some secret kamikaze mission. ::)

Title: Re: Checkers
Post by mikedagr8 on May 12^th, 2008, 4:16am

on 05/12/08 at 04:13:07, ThudanBlunder wrote:

Yes, we can assume Red is trying to crown and is not on some secret kamikaze mission. ::)

So I guess we can assume then that white IS on some secret kamikaze mission. ;D

Title: Re: Checkers
Post by towr on May 12^th, 2008, 4:32am

19-24
30-25, 21-30
29-25, 30-21
31-27, 24-31 and the game is over before red can crown

Title: Re: Checkers
Post by ThudanBlunder on May 12^th, 2008, 4:44am

on 05/12/08 at 04:32:33, towr wrote:

19-24
30-25, 21-30
29-25, 30-21
31-27, 24-31 and the game is over before red can crown

Interesting. But that's not what I had in mind.
The game is over when the last man is captured.
And the last man is captured after Red crowns with 24-31.

Title: Re: Checkers
Post by rmsgrey on May 12^th, 2008, 5:24am

For #2 (using ##-## for a normal move, and ##x##[x##[x##[...]] for a [multiple] capture):

1) - 19-24
[hide]2) 29-25 24-28......
3) 30-26 21x30x23
4) 31-26 23x30......[/hide]

But, it is indeed possible for red to crown the next man he moves - the real question is whether it's possible for white to prevent him.

Title: Re: Checkers
Post by ThudanBlunder on May 12^th, 2008, 5:35am

on 05/12/08 at 05:24:06, rmsgrey wrote:

But, it is indeed possible for red to crown the next man he moves

The original question assumes 'against best play'. I thought that was obvious.

Your 3rd move for Red is illegal.

Title: Re: Checkers
Post by Sealock on May 12^th, 2008, 6:38am

on 05/12/08 at 05:35:47, ThudanBlunder wrote:

The original question assumes 'against best play'. I thought that was obvious.

"Best play" for white is not to throw pieces in front of red's left-hand piece in order to prevent the right-hand one from getting a chance to be kinged, but I now understand how the problem works if white actively tries to prevent red kinging the first piece he moves (as though he has made a bet with red saying that he can't do so).

The solution is a variation on rmsgrey's attempt:
[hideb]If red makes a first move other than 19-24, the piece he moves is easily captured in one or two moves, thus preventing him from kinging the desired piece. Otherwise,
1) - 19-24
2) 29-25 24-28 (red's other choice here, 24-27, leads to capture)
3) 30-26 21x30 (the rules require red to capture the available piece)
4) 31-27 30x23x32 (here, again, red's hand is forced)

and the game ends without red's rightmost piece being kinged.[/hideb]

Title: Re: Checkers
Post by ThudanBlunder on May 12^th, 2008, 6:47am

on 05/12/08 at 06:38:43, Sealock wrote:

"Best play" for white is not to throw pieces in front of red's left-hand piece in order to prevent the right-hand one from getting a chance to be kinged...[/hideb]

'Best play' depends upon the objective, and the objective here has been spelt out by me ad nauseum.

Anyway, it seems you have the solution. So it wasn't so difficult after all, was it? ;)

Welcome to the forum, by the way.

Title: Re: Checkers
Post by Obob on May 12^th, 2008, 8:54am

Whats the argument that red can't play 19-23? That seemed to be trickier to me.

Title: Re: Checkers
Post by ThudanBlunder on May 12^th, 2008, 8:59am

on 05/12/08 at 08:54:36, Obob wrote:

Whats the argument that red can't play 19-23? That seemed to be trickier to me.

19-23 is also answered by 29-25

Title: Re: Checkers
Post by Hippo on May 12^th, 2008, 10:10am

on 05/11/08 at 03:19:08, ThudanBlunder wrote:

2) Is it possible for him to crown the next man he moves?

From the responses I guess "the NEXT" is equivalent "the FIRST" not "the SECOND" I have expected. So

on 05/11/08 at 12:43:33, Hippo wrote:

2)
1. ... 21-25
2. ?x? 19-24
3. ..? 24-28
4. ..? 28-32

Is not the solution ;)

So for 1) if I understand it well ;) ... place your piece anywhere into the middle of the board and opponent pieces diagonally around your one. He cannot capture yours and you will capture unmoved piece. With one piece according the parity he will never capture your piece so you win the bet (He has to escape to the white corner not even to loose the game).

Title: Re: Checkers
Post by iono on May 12^th, 2008, 9:52pm

you have to capture when possible. That ruled helped me win an important game before.

Title: Re: Checkers
Post by ThudanBlunder on May 12^th, 2008, 10:32pm

on 05/12/08 at 21:52:16, iono wrote:

you have to capture when possible.

If I don't capture will you start huffing? :P

Title: Re: Checkers
Post by Barukh on May 13^th, 2008, 6:16am

It's a pitty I overlooked this interesting thread...

By the way, why this is invalid:

on 05/12/08 at 05:24:06, rmsgrey wrote:

[hide]3) ... 21x30x23[/hide]

while this is valid:

on 05/12/08 at 06:38:43, Sealock wrote:

[hide]4) ... 30x23x32[/hide]

Title: Re: Checkers
Post by ThudanBlunder on May 13^th, 2008, 6:23am

on 05/13/08 at 06:16:29, Barukh wrote:

By the way, why this is invalid:

Because coronations are conducted at a stately pace and should not be hurried in order to satisfy the new monarch's bloodlust. :P
(Legally, because the move is deemed over when the man is crowned.)

on 05/13/08 at 06:16:29, Barukh wrote:

It's a pitty I overlooked this interesting thread...

Don't worry, I have a third part. :)

Title: Re: Checkers
Post by Hippo on May 13^th, 2008, 6:49am

on 05/13/08 at 06:16:29, Barukh wrote:

It's a pitty I overlooked this interesting thread...

By the way, why this is invalid:

while this is valid:

There is a lot of variants of checkers so the best start for such a puzzle is to define the rules.

Title: Re: Checkers
Post by Grimbal on May 13^th, 2008, 7:53am

Is it mandatory to eat 2 if you have the choice between eating 1 or 2?

Title: Re: Checkers
Post by Barukh on May 13^th, 2008, 9:23am

on 05/13/08 at 06:23:53, ThudanBlunder wrote:

Don't worry, I have a third part. :)

Was the first part solved?

[hide]18 vs 15, 22[/hide].

Title: Re: Checkers
Post by ThudanBlunder on May 13^th, 2008, 12:06pm

on 05/12/08 at 10:10:47, Hippo wrote:

So for 1) if I understand it well ;) ... place your piece anywhere into the middle of the board and opponent pieces diagonally around your one. He cannot capture yours and you will capture unmoved piece. With one piece according the parity he will never capture your piece so you win the bet (He has to escape to the white corner not even to loose the game).

Oh, I hadn't considered this. This also draws easily. Well done.

on 05/13/08 at 07:53:27, Grimbal wrote:

Is it mandatory to eat 2 if you have the choice between eating 1 or 2?

Yes.

on 05/13/08 at 09:23:50, Barukh wrote:

Was the first part solved?

[hide]18 vs 15, 22[/hide].

Yes, I think that's what Hippo meant, too. Well done.
But I think if I had set them up like that the guy might not have paid up, as it is a well-known trap!
So the first part is not yet solved satisfactorily.

on 05/13/08 at 06:49:44, Hippo wrote:

There is a lot of variants of checkers so the best start for such a puzzle is to define the rules.

I agree:

on 05/11/08 at 03:19:08, ThudanBlunder wrote:

Here are a few checkers problems.
The rules are as in US and UK: 8x8 board, only kings can move backwards one square, and of course capturing is compulsory.

I wasn't aware until I just looked it up that in International Checkers newly-crowned kings can continue capturing. [In fact, from Wikipedia it seems that in this case the man continues capturing without being crowned. A piece is crowned if it stops on the far edge of the board at the end of its turn (that is, not if it reaches the edge but must then jump another piece backward).] But, having stated which rules are in use, I don't think it is incumbent upon me to highlight every possible difference between variants.

Title: Re: Checkers
Post by temporary on May 13^th, 2008, 4:41pm

It is not mandatory take more pieces when forked, but it is mandatory to still do any captures possible.

Title: Re: Checkers
Post by Barukh on May 14^th, 2008, 10:27am

on 05/13/08 at 12:06:51, ThudanBlunder wrote:

But I think if I had set them up like that the guy might not have paid up, as it is a well-known trap!
So the first part is not yet solved satisfactorily.

Hmm... What does the theory say about general positions? Is 2 Red kings vs 1 White king a win for Red (according to UK rules)?

???

Title: Re: Checkers
Post by ThudanBlunder on May 14^th, 2008, 12:09pm

on 05/14/08 at 10:27:38, Barukh wrote:

Hmm... What does the theory say about general positions? Is 2 Red kings vs 1 White king a win for Red (according to UK rules)?
???

Yes, according to any rules the two kings can force the lone king out of a double corner and win.

Title: Re: Checkers
Post by temporary on May 18^th, 2008, 5:58pm

Unless the single king can move between the other two kings and neither of them is on an edge.

Title: Re: Checkers
Post by ThudanBlunder on May 19^th, 2008, 4:33am

on 05/18/08 at 17:58:54, temporary wrote:

Unless the single king can move between the other two kings and neither of them is on an edge.

If you bothered to read threads before degrading them with your redundant comments, you would realize that this case has already been covered by three posters, including myself.

Title: Re: Checkers
Post by temporary on May 20^th, 2008, 7:08pm

Did you just call yourself a poster? *chuckles*