Riddle and Puzzle Thread

[M2R]

I would choose to play first.

Playing down to a two chip size opening on the table, I play my chip in  the middle of the two chip size area leaving him with no play on either end.

Playing down to a three chip size opening on the table, I play the middle chip size square forcing him to play either end. Leaving me to play the last chip.

Playing down to a four (4X1) chip size opening on the table, I play my chip covering the middle two chip sized squares forcing him to play either end. Leaving me to play the last chip. If the table opening is 2X2 then simply play to the very centre.

Playing down to a five (5X1) chip size opening on the table, I play my chip in the centre so as to leave two chip sized squares on either side.  If my opponent covers two chip size squares, I do the same. If my opponent only covers one chip size square on one side, I do the same on the other side. Either way the end is forced.

Regardless of table size the goal will be to play until the remaining open space on the table represents one of the above sizes that can be forced.

Basically the idea is that by playing first I secure the advantage of either covering 1, 2 or 4 squares at a time which should give me the advantage. Seems too complicated to be correct though.

[iacas]

Seems too complicated to be correct though.

You're correct… in that your answer is not correct. You can't guarantee at all that you're the one being left the "areas" you mentioned. The solution is far more elegant. The solution also absolutely guarantees your victory.

[dkmago]

Choose how plays first.  If there's an even number of chips that fit on the table greater than 2, you go first.  If an odd number of chips fit, then your opponent goes first.  (I think).

[iacas]

Choose how plays first.  If there's an even number of chips that fit on the table greater than 2, you go first.  If an odd number of chips fit, then your opponent goes first.  (I think).

No. Chips don't have to be placed touching anything. Thus there is no set number that you can calculate.

[billchao]

Here's an old one:

A friend of yours is a big gambler. He decides one day to bet you everything you have for everything he has in a simple game. You're a gambler too so you go along.

The rules of the game are simple. You're each given identically sized poker chips and a flat, rectangular table on which to play. You'll alternate turns placing one poker chip down per turn, with the stipulation that the poker chip must rest completely flat on the table (no hanging over the edge, no overlapping other chips, no standing poker chips on their edges - you also can't move any poker chips once placed), and that you lose when you cannot make a legal play.

Your friend (stupidly) offers you the choice of deciding who makes the first move OR to pick the size of the table. He'll make the other choice.

Which do choice do you take, what do you choose, and why?

Go first. Put your first chip flatly on top of your opponent's stack.

[iacas]

Go first. Put your first chip flatly on top of your opponent's stack.

Nope. Not a legal move - chips must go on the table. And the chips are all the same anyway. If nobody has the correct answer, I'll share it tomorrow before noon or so.

[tmac20]

Choose to go second... Wherever your opponent places his chip, place yours on the exact opposite end.

[iacas]

Choose to go second... Wherever your opponent places his chip, place yours on the exact opposite end.

Close. But no.

[Lihu]

Here's an old one:

A friend of yours is a big gambler. He decides one day to bet you everything you have for everything he has in a simple game. You're a gambler too so you go along.

The rules of the game are simple. You're each given identically sized poker chips and a flat, rectangular table on which to play. You'll alternate turns placing one poker chip down per turn, with the stipulation that the poker chip must rest completely flat on the table (no hanging over the edge, no overlapping other chips, no standing poker chips on their edges - you also can't move any poker chips once placed), and that you lose when you cannot make a legal play.

Your friend (stupidly) offers you the choice of deciding who makes the first move OR to pick the size of the table. He'll make the other choice.

Which do choice do you take, what do you choose, and why?

Choose the order. It appears that even or odd numbers of chips does not matter, because you and he times the number that fit (any number) is always an even number.

[iacas]

Choose the order. It appears that even or odd numbers of chips does not matter, because you and he times the number that fit (any number) is always an even number.

Nope. You can change the number of chips that fit by changing where you put them. One chip can take up space for one chip or space for four chips.

Consider a 2 x 2 space - you could fit any number of chips there from 4 to 3 to 2 to 1:

If that was the last space left on the board, the only way to guarantee your victory would be to put the one in the middle… but you'd have to somehow guarantee that you have a 2 x 2 spot left on the board AND that it was your turn. In other words, that's not gonna happen.

[Lihu]

Quote:

Originally Posted by Lihu

Choose the order. It appears that even or odd numbers of chips does not matter, because you and he times the number that fit (any number) is always an even number.

Nope. You can change the number of chips that fit by changing where you put them. One chip can take up space for one chip or space for four chips.

Consider a 2 x 2 space - you could fit any number of chips there from 4 to 3 to 2 to 1:

If that was the last space left on the board, the only way to guarantee your victory would be to put the one in the middle… but you'd have to somehow guarantee that you have a 2 x 2 spot left on the board AND that it was your turn. In other words, that's not gonna happen.

It seems like those are examples of less optimum use of the space available on the table than a packed scheme (chips arranged such that they are tangent to their immediate neighbor). So, if the table size is the same, the packed scheme will always allow you more turns than a non efficient scheme.

So, if he and you use the most efficient schemes it will maximize the number of turns, and you are left with always having an even number of turns. If he chooses to use a scheme less efficient than the packed scheme, while you elect to use it, you will always have more turns than him.

Or, did I read the problem statement incorrectly?

[14ledo81]

I tried cheating (was not going to post pretending to know the answer). I googled "poker chip and table riddle". This thread was at the top. LOL.. so much for my cheating.

[Welkin]

Go first, no matter how big or small the table is you should be the first one to have a spot left that you can either place your chip in the centre leaving no legal move (like in the picture) or divide it into two spaces with enough space for only one chip in each.

[Abu3baid]

Ok.. thought about it some more.. I will choose to go second and let him pick the size of the table and go first. No matter what size of table, coffee or poker table he picks when ever he puts a chip down I will put my chip right next to his (top,bottom,left,under,diagonal) it doesn't really matter in the end, what I see happening is that by the time he puts the last chip down I will always have room for my chip no matter what and he will always end up with no where to go...

[iacas]

It seems like those are examples of less optimum use of the space available on the table than a packed scheme (chips arranged such that they are tangent to their immediate neighbor). So, if the table size is the same, the packed scheme will always allow you more turns than a non efficient scheme.

You get to place them however you'd like. You're not obligated to use the packed scheme (you could get more packed by offsetting the second row half a chip, if the space around allowed for that).

There's no guarantee at all that he'll use an "efficient" scheme. His goal is to win.

Go first, no matter how big or small the table is you should be the first one to have a spot left that you can either place your chip in the centre leaving no legal move (like in the picture) or divide it into two spaces with enough space for only one chip in each.

There's no real guarantee that you'll end up with a 3x1 spot. He could see that coming from earlier on and thwart your plans by adjusting his spacing.

No matter what size of table, coffee or poker table he picks when ever he puts a chip down I will put my chip right next to his (top,bottom,left,under,diagonal) it doesn't really matter in the end, what I see happening is that by the time he puts the last chip down I will always have room for my chip no matter what and he will always end up with no where to go...

Nope.

Answer coming soon. It's quite clever and some of you have been on the right track, but you're missing out on how random the other player could play, and how there's only really one way to force his hand by choosing table size or playing order properly.

[David in FL]

Ok.. thought about it some more.. I will choose to go second and let him pick the size of the table and go first.

No matter what size of table, coffee or poker table he picks when ever he puts a chip down I will put my chip right next to his (top,bottom,left,under,diagonal) it doesn't really matter in the end, what I see happening is that by the time he puts the last chip down I will always have room for my chip no matter what and he will always end up with no where to go...

Even if he picks a table 1 chip wide by 5 chips long......?

The problem is the unknown.  Whatever benefit there is from picking the table is negated by the ability to either take the first move or force the other guy to do so.  Therefore, I think the right answer has to be to keep the choice of moves for yourself, but whatever the "plan" is, it must work for a table of any dimension, because again, you have no control over what he picks.  It could be anything.

The only way I can make it work, is if I tell him that I'll pick the table, and then let the dummy pick the order of play before I actually lay out the table.  Then the challenge becomes building a table that you can guarantee a win on when he goes first......if you go first it's as simple as a one chip square table.

I'll keep thinking.....on my way to a Sea World for my daughter's birthday party.....

[Welkin]

I thought about side by side but if it gets down to the 2x2 and you place your chip next to his you're leaving him the option of spacing the last chip and leaving you no room. I think regardless of size there's only one critical turn, you can block a 2x2 space with your last turn and so if its just a little bigger you need to play it so that he can't do the same on his turn. If you place a chip in a corner of a 2x2 space there's no way to make the next play the last one and so if its just a little bigger you keep to the edges and force him to leave you that 2x2 or smaller space?

By the way hope its ok for a newbie to be joining in, I will be posting about golf here as well I promise

[iacas]

Then the challenge becomes building a table that you can guarantee a win on when he goes first......if you go first it's as simple as a one chip square table.

They're normal tables. You missed a post above. :) Coffee table, banquet table, whatever. A regular table. Not a one-chip table.