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Subject: My RPN version of the game rss

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Ted Alper
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OK, this actually works reasonably well! [and, seeing as the kickstarter reprint will have a "math geek" extra set of cards, I want to point out that this could adapt to unary operators more easily than the current game, though I guess it has other drawbacks in terms of its universal appeal. And how often would a square root or factorial operator be useful? I guess I need to run the simulation...]

Shuffle all 36 cards, and lay them out without regard to the checkerboard (that is, don't alternate numbers and operations, just put them all in the grid randomly mixed together). For this version, you also have to allow paths to go on diagonals, not just vertically and horizontally. Evaluate everything in RPN notation The 6x6 board has 32520 possible paths allowing diagonals, but in general, only about 2000-2500 are valid RPN expressions (assuming the original mix of cards and all operators are binary) -- this is roughly comparable to the original game's number of expressions (which benefit from associativity of the operators). You can usually get all or almost all the numbers from 1 to 40, same as in the original version.
 
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Ted Alper
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Allowing movement on diagonals but RPN notation, you can get 26 as:
Spoiler (click to reveal)

13 9 4 + wild(+)
or 7 4 x 2 wild(-)
or10 14 wild(+) 2 +
or 8 5 x 14 wild (-)
13 9 7 - wild(x)
or 9 4 + 2 x [finally, one without the wild card, though could use it for either operator]
or 8 5 + 2 x (could use WILD for either operator)
or 8 14 + 4 + (could use WILD for either operator)
or 14 1 - 13 +
or 14 1 x 12 +
I think those are all the ways up to minor permutations that use WILD as either +, -, or x. there might be others with WILD as other operators
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Ted Alper
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At home, there aren't that many people to play with since my oldest graduated high school. Gary's a pretty smart cat, but not that smart.

this is the same board as in the last image, but the target is 33.

there are essentially 7 ways to get it, not including minor permutations and only using wild as +,-, or x.




Spoiler (click to reveal)

8 5 - 11 x
11 8 14 wild +
11 8 5 - x
13 6 + 14 wild
1 10 + 3 x
3 10 1 + x
3 3 10 x +
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lotus dweller
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So this game will work for prefix, infix, and postfix notations.
There are 5 new terms for me today. (Including RPN and PN.)
 
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Ted Alper
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Pinook wrote:
So this game will work for prefix, infix, and postfix notations.
There are 5 new terms for me today. (Including RPN and PN.)


I hadn't thought about PN, though I'm not sure it adds anything to RPN in game terms, since any path on the board that is a well-formed RPN expression would give the same result in PN just by traversing it backward.

But you can actually come up with multiple variants for the game by controlling 4 parameters independently [not even counting house rules about what operations the WILD operator can use]:

(A) do you deal out the board with all the cards mixed together randomly, or do you separate numbers and operators and alternate them in a checkerboard pattern?
boolean checkerboard = true; //original game

(B) do you generate the path of five squares on the board allowing diagonals as well as right/left/up/down, or do you only allow right/left/up/down?
boolean diagonals = false; //original game

(C)do you evaluate expressions with RPN or infix notation [or PN, sure] or you could even allow both types of solutions to be valid.
boolean infix_allowed = true; //original game
boolean RPN_allowed = false; //original game


Maybe they aren't completely independent, since some combinations don't make sense -- you have to allow at least ONE of infix/RPN [or PN], for example, and if you use a checkerboard pattern and don't allow diagonals, there won't be *any* legal RPN expressions, etc. And a few others are POSSIBLE but result in pretty tough games with many unattainable numbers -- if checkerboard=false and diagonals=false, the game is pretty tough. But there are still a lot of plausible games here, with different levels of difficulty.
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