I have an idea for an app that a friend of mine has implemented in CSS: http://mathenchant.org/chipchip/ I’d be interested in people’s comments. Is it fun to play? Are the directions clear? I’m aware of glitches in the implementation (some of which are browser-specific or platform-specific), and do let me know about them, but those are of secondary interest; what I really want is ideas for making the app more fun, and (from those of you with some relevant experience) a sense of whether the game has commercial potential. The page runs on laptops and smartphones. If the boundaries between tiles aren't clear, try a different browser (and let me know about the issue). ChipChip started out as a math game, but James Tanton pointed out that there’s a much bigger market for anagram-syle word-games. So you can play in either Number Mode (the goal is to sort the numbered tiles into ascending order) or Word Mode (the goal is to spell a word). I specifically chose words with no repeated letters; do you think it would be more fun if I dropped this constraint? Jim Propp
Very interesting. After playing a couple dozen games, I seem to be able to consistently get "0 over par", although I don't have a conscious strategy. How does it determine 'par'? Does it have an algorithm for a solution? On Thu, Jul 21, 2016 at 1:43 PM, James Propp <jamespropp@gmail.com> wrote:
I have an idea for an app that a friend of mine has implemented in CSS: http://mathenchant.org/chipchip/ I’d be interested in people’s comments. Is it fun to play? Are the directions clear?
I’m aware of glitches in the implementation (some of which are browser-specific or platform-specific), and do let me know about them, but those are of secondary interest; what I really want is ideas for making the app more fun, and (from those of you with some relevant experience) a sense of whether the game has commercial potential.
The page runs on laptops and smartphones. If the boundaries between tiles aren't clear, try a different browser (and let me know about the issue).
ChipChip started out as a math game, but James Tanton pointed out that there’s a much bigger market for anagram-syle word-games. So you can play in either Number Mode (the goal is to sort the numbered tiles into ascending order) or Word Mode (the goal is to spell a word). I specifically chose words with no repeated letters; do you think it would be more fun if I dropped this constraint?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
If you sum (with multiplicity) the squares of the positions of the tiles, and divide by 2, you get a quantity that goes up by 1 when you explode and goes down by 1 when you unexplode. (To check this, note that if you subtract a^2+b^2 from (a-1)^2+(b+1)^2 you get 2+2a-2b, which equals 2 if a=b and equals -2 if a=b-2.) This gives us an easy way to compute par, *if* there's a way to get from the initial state to the final state without using any unexplode moves. Most of the puzzles can be done without using any unexplode moves. This analysis also tells us that you can achieve 0 over par, 2 over par, 4 over par, ... but not 1 over part, 3 over part, 5 over par, ... The only unfailing algorithm I know for these puzzles is brute force. Jim Propp On Thu, Jul 21, 2016 at 7:10 PM, Paul Palmer <paul.allan.palmer@gmail.com> wrote:
Very interesting.
After playing a couple dozen games, I seem to be able to consistently get "0 over par", although I don't have a conscious strategy.
How does it determine 'par'? Does it have an algorithm for a solution?
On Thu, Jul 21, 2016 at 1:43 PM, James Propp <jamespropp@gmail.com> wrote:
I have an idea for an app that a friend of mine has implemented in CSS: http://mathenchant.org/chipchip/ I’d be interested in people’s comments. Is it fun to play? Are the directions clear?
I’m aware of glitches in the implementation (some of which are browser-specific or platform-specific), and do let me know about them, but those are of secondary interest; what I really want is ideas for making the app more fun, and (from those of you with some relevant experience) a sense of whether the game has commercial potential.
The page runs on laptops and smartphones. If the boundaries between tiles aren't clear, try a different browser (and let me know about the issue).
ChipChip started out as a math game, but James Tanton pointed out that there’s a much bigger market for anagram-syle word-games. So you can play in either Number Mode (the goal is to sort the numbered tiles into ascending order) or Word Mode (the goal is to spell a word). I specifically chose words with no repeated letters; do you think it would be more fun if I dropped this constraint?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
This puzzle appears to be mostly dominated by shape; the flexibility on explode means that from a given shape you can often get the ordering you need easily. The eccentricity of the state graph from the goal state appears to be equal to or close to that of just the shape graph (the same puzzle but completely ignoring letters and numbers). For odd sizes, the hardest shape is a single centered vertical stack. At n=9, the hardest position both just considering shape and considering both numbers and shape is a single centered vertical stack (I'm somewhat surprised this is harder than just the reversed numbers). The distance from goal is 30. Contrast n=5, where the hardest shape is the centered stack with a distance of 5, but the hardest position is (5,4,3,2,1) with a distance of 8 (or two other related positions). I believe iterated depth-first search with the two separate heuristics, one by the shape, the other by the sum of the distances of the numbers from their homes, will give you an optimal solver that works pretty well. On Thu, Jul 21, 2016 at 4:58 PM, James Propp <jamespropp@gmail.com> wrote:
If you sum (with multiplicity) the squares of the positions of the tiles, and divide by 2, you get a quantity that goes up by 1 when you explode and goes down by 1 when you unexplode. (To check this, note that if you subtract a^2+b^2 from (a-1)^2+(b+1)^2 you get 2+2a-2b, which equals 2 if a=b and equals -2 if a=b-2.)
This gives us an easy way to compute par, *if* there's a way to get from the initial state to the final state without using any unexplode moves. Most of the puzzles can be done without using any unexplode moves.
This analysis also tells us that you can achieve 0 over par, 2 over par, 4 over par, ... but not 1 over part, 3 over part, 5 over par, ...
The only unfailing algorithm I know for these puzzles is brute force.
Jim Propp
On Thu, Jul 21, 2016 at 7:10 PM, Paul Palmer <paul.allan.palmer@gmail.com> wrote:
Very interesting.
After playing a couple dozen games, I seem to be able to consistently get "0 over par", although I don't have a conscious strategy.
How does it determine 'par'? Does it have an algorithm for a solution?
On Thu, Jul 21, 2016 at 1:43 PM, James Propp <jamespropp@gmail.com> wrote:
I have an idea for an app that a friend of mine has implemented in CSS: http://mathenchant.org/chipchip/ I’d be interested in people’s comments. Is it fun to play? Are the directions clear?
I’m aware of glitches in the implementation (some of which are browser-specific or platform-specific), and do let me know about them, but those are of secondary interest; what I really want is ideas for making the app more fun, and (from those of you with some relevant experience) a sense of whether the game has commercial potential.
The page runs on laptops and smartphones. If the boundaries between tiles aren't clear, try a different browser (and let me know about the issue).
ChipChip started out as a math game, but James Tanton pointed out that there’s a much bigger market for anagram-syle word-games. So you can play in either Number Mode (the goal is to sort the numbered tiles into ascending order) or Word Mode (the goal is to spell a word). I specifically chose words with no repeated letters; do you think it would be more fun if I dropped this constraint?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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There is one pretty good challenge, at least I found it hard. Solve one of the puzzles for n=9 (doesn't matter which one.) Now try to stack everything up in the center in one pile, in only 30 more moves. On Thu, Jul 21, 2016 at 6:53 PM, Tom Rokicki <rokicki@gmail.com> wrote:
This puzzle appears to be mostly dominated by shape; the flexibility on explode means that from a given shape you can often get the ordering you need easily.
The eccentricity of the state graph from the goal state appears to be equal to or close to that of just the shape graph (the same puzzle but completely ignoring letters and numbers). For odd sizes, the hardest shape is a single centered vertical stack. At n=9, the hardest position both just considering shape and considering both numbers and shape is a single centered vertical stack (I'm somewhat surprised this is harder than just the reversed numbers). The distance from goal is 30.
Contrast n=5, where the hardest shape is the centered stack with a distance of 5, but the hardest position is (5,4,3,2,1) with a distance of 8 (or two other related positions).
I believe iterated depth-first search with the two separate heuristics, one by the shape, the other by the sum of the distances of the numbers from their homes, will give you an optimal solver that works pretty well.
On Thu, Jul 21, 2016 at 4:58 PM, James Propp <jamespropp@gmail.com> wrote:
If you sum (with multiplicity) the squares of the positions of the tiles, and divide by 2, you get a quantity that goes up by 1 when you explode and goes down by 1 when you unexplode. (To check this, note that if you subtract a^2+b^2 from (a-1)^2+(b+1)^2 you get 2+2a-2b, which equals 2 if a=b and equals -2 if a=b-2.)
This gives us an easy way to compute par, *if* there's a way to get from the initial state to the final state without using any unexplode moves. Most of the puzzles can be done without using any unexplode moves.
This analysis also tells us that you can achieve 0 over par, 2 over par, 4 over par, ... but not 1 over part, 3 over part, 5 over par, ...
The only unfailing algorithm I know for these puzzles is brute force.
Jim Propp
On Thu, Jul 21, 2016 at 7:10 PM, Paul Palmer <paul.allan.palmer@gmail.com
wrote:
Very interesting.
After playing a couple dozen games, I seem to be able to consistently get "0 over par", although I don't have a conscious strategy.
How does it determine 'par'? Does it have an algorithm for a solution?
On Thu, Jul 21, 2016 at 1:43 PM, James Propp <jamespropp@gmail.com> wrote:
I have an idea for an app that a friend of mine has implemented in CSS: http://mathenchant.org/chipchip/ I’d be interested in people’s comments. Is it fun to play? Are the directions clear?
I’m aware of glitches in the implementation (some of which are browser-specific or platform-specific), and do let me know about them, but those are of secondary interest; what I really want is ideas for making the app more fun, and (from those of you with some relevant experience) a sense of whether the game has commercial potential.
The page runs on laptops and smartphones. If the boundaries between tiles aren't clear, try a different browser (and let me know about the issue).
ChipChip started out as a math game, but James Tanton pointed out that there’s a much bigger market for anagram-syle word-games. So you can play in either Number Mode (the goal is to sort the numbered tiles into ascending order) or Word Mode (the goal is to spell a word). I specifically chose words with no repeated letters; do you think it would be more fun if I dropped this constraint?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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-- -- http://cube20.org/ -- [ <http://golly.sf.net/>Golly link suppressed; ask me why] --
One feature of all these puzzles is that if you treat the tiles as indistinguishable, there's no way to lose; EVERY sequence of explode operations will take you to the same end state, and in the same number of moves every time! This is called the confluence property of the abelian sandpile mode (though some people call it "the abelian property", which I think is a mistake). Jim On Thursday, July 21, 2016, Tom Rokicki <rokicki@gmail.com> wrote:
This puzzle appears to be mostly dominated by shape; the flexibility on explode means that from a given shape you can often get the ordering you need easily.
The eccentricity of the state graph from the goal state appears to be equal to or close to that of just the shape graph (the same puzzle but completely ignoring letters and numbers). For odd sizes, the hardest shape is a single centered vertical stack. At n=9, the hardest position both just considering shape and considering both numbers and shape is a single centered vertical stack (I'm somewhat surprised this is harder than just the reversed numbers). The distance from goal is 30.
Contrast n=5, where the hardest shape is the centered stack with a distance of 5, but the hardest position is (5,4,3,2,1) with a distance of 8 (or two other related positions).
I believe iterated depth-first search with the two separate heuristics, one by the shape, the other by the sum of the distances of the numbers from their homes, will give you an optimal solver that works pretty well.
On Thu, Jul 21, 2016 at 4:58 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
If you sum (with multiplicity) the squares of the positions of the tiles, and divide by 2, you get a quantity that goes up by 1 when you explode and goes down by 1 when you unexplode. (To check this, note that if you subtract a^2+b^2 from (a-1)^2+(b+1)^2 you get 2+2a-2b, which equals 2 if a=b and equals -2 if a=b-2.)
This gives us an easy way to compute par, *if* there's a way to get from the initial state to the final state without using any unexplode moves. Most of the puzzles can be done without using any unexplode moves.
This analysis also tells us that you can achieve 0 over par, 2 over par, 4 over par, ... but not 1 over part, 3 over part, 5 over par, ...
The only unfailing algorithm I know for these puzzles is brute force.
Jim Propp
On Thu, Jul 21, 2016 at 7:10 PM, Paul Palmer < paul.allan.palmer@gmail.com <javascript:;>> wrote:
Very interesting.
After playing a couple dozen games, I seem to be able to consistently get "0 over par", although I don't have a conscious strategy.
How does it determine 'par'? Does it have an algorithm for a solution?
On Thu, Jul 21, 2016 at 1:43 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
I have an idea for an app that a friend of mine has implemented in CSS: http://mathenchant.org/chipchip/ I’d be interested in people’s comments. Is it fun to play? Are the directions clear?
I’m aware of glitches in the implementation (some of which are browser-specific or platform-specific), and do let me know about them, but those are of secondary interest; what I really want is ideas for making the app more fun, and (from those of you with some relevant experience) a sense of whether the game has commercial potential.
The page runs on laptops and smartphones. If the boundaries between tiles aren't clear, try a different browser (and let me know about the issue).
ChipChip started out as a math game, but James Tanton pointed out that there’s a much bigger market for anagram-syle word-games. So you can play in either Number Mode (the goal is to sort the numbered tiles into ascending order) or Word Mode (the goal is to spell a word). I specifically chose words with no repeated letters; do you think it would be more fun if I dropped this constraint?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Here's my "Sorting-by-Avalanche Conjecture": If you put tiles numbered 1 through 2n in a single column, then as long as you only perform exploding moves, AND as long as each exploding move sends a smaller-numbered tile to the left and a larger-numbered tile to the right, then you can't go wrong! You're guaranteed to end up with the 2n chips sorted into numerical order (with a single empty column in the middle). However, if we replace 2n by 2n+1, this kind of confluence does not occur. Here's an amusing consequence of the two preceding paragraphs: If you have an odd number of tiles, assigned numbers between 1 and 2n-1, and you start sorting them in this fashion, they won't all end up sorted. But if you now place a tile numbered 2n in the middle and continue sorting in this fashion, the tiles must all end up sorted into numerical order. Another consequence of the conjecture (relevant to the ChipChip app) is that when you start out with 2n+1 tiles in a single column, you can't go wrong as long as you never move tile n. Various clever people have worked on this conjecture, but nobody has found a proof. I stress that this all assumes you follow the rule that when you perform an exploding move that sends tile i to the left and tile j to the right, i must be less than j. I know very little about what happens when you allow unexploding moves; I included them in the app because I thought it would make it more fun, not because it's related to the theory. All of this grew out of the theory of chip-firing that started with work of Arthur Engel in the early 70s. Jim Propp On Thu, Jul 21, 2016 at 11:35 PM, James Propp <jamespropp@gmail.com> wrote:
One feature of all these puzzles is that if you treat the tiles as indistinguishable, there's no way to lose; EVERY sequence of explode operations will take you to the same end state, and in the same number of moves every time! This is called the confluence property of the abelian sandpile mode (though some people call it "the abelian property", which I think is a mistake).
Jim
On Thursday, July 21, 2016, Tom Rokicki <rokicki@gmail.com> wrote:
This puzzle appears to be mostly dominated by shape; the flexibility on explode means that from a given shape you can often get the ordering you need easily.
The eccentricity of the state graph from the goal state appears to be equal to or close to that of just the shape graph (the same puzzle but completely ignoring letters and numbers). For odd sizes, the hardest shape is a single centered vertical stack. At n=9, the hardest position both just considering shape and considering both numbers and shape is a single centered vertical stack (I'm somewhat surprised this is harder than just the reversed numbers). The distance from goal is 30.
Contrast n=5, where the hardest shape is the centered stack with a distance of 5, but the hardest position is (5,4,3,2,1) with a distance of 8 (or two other related positions).
I believe iterated depth-first search with the two separate heuristics, one by the shape, the other by the sum of the distances of the numbers from their homes, will give you an optimal solver that works pretty well.
On Thu, Jul 21, 2016 at 4:58 PM, James Propp <jamespropp@gmail.com> wrote:
If you sum (with multiplicity) the squares of the positions of the tiles, and divide by 2, you get a quantity that goes up by 1 when you explode and goes down by 1 when you unexplode. (To check this, note that if you subtract a^2+b^2 from (a-1)^2+(b+1)^2 you get 2+2a-2b, which equals 2 if a=b and equals -2 if a=b-2.)
This gives us an easy way to compute par, *if* there's a way to get from the initial state to the final state without using any unexplode moves. Most of the puzzles can be done without using any unexplode moves.
This analysis also tells us that you can achieve 0 over par, 2 over par, 4 over par, ... but not 1 over part, 3 over part, 5 over par, ...
The only unfailing algorithm I know for these puzzles is brute force.
Jim Propp
On Thu, Jul 21, 2016 at 7:10 PM, Paul Palmer < paul.allan.palmer@gmail.com> wrote:
Very interesting.
After playing a couple dozen games, I seem to be able to consistently get "0 over par", although I don't have a conscious strategy.
How does it determine 'par'? Does it have an algorithm for a solution?
On Thu, Jul 21, 2016 at 1:43 PM, James Propp <jamespropp@gmail.com> wrote:
I have an idea for an app that a friend of mine has implemented in CSS: http://mathenchant.org/chipchip/ I’d be interested in people’s comments. Is it fun to play? Are the directions clear?
I’m aware of glitches in the implementation (some of which are browser-specific or platform-specific), and do let me know about them, but those are of secondary interest; what I really want is ideas for making the app more fun, and (from those of you with some relevant experience) a sense of whether the game has commercial potential.
The page runs on laptops and smartphones. If the boundaries between tiles aren't clear, try a different browser (and let me know about the issue).
ChipChip started out as a math game, but James Tanton pointed out that there’s a much bigger market for anagram-syle word-games. So you can play in either Number Mode (the goal is to sort the numbered tiles into ascending order) or Word Mode (the goal is to spell a word). I specifically chose words with no repeated letters; do you think it would be more fun if I dropped this constraint?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (3)
-
James Propp -
Paul Palmer -
Tom Rokicki