2 more difficulty ideas: Medium Easy: set attributes for Rogue, Paladin, Shaman and Pay-to-win so that Pay-to-win wins all three, the rest win 1 and lose 2.
Medium Hard: set attributes for Rogue, Paladin, Shaman and All-rounder so that All-rounder ties all 3, the rest win 1, lose 1, and tie 1.
You can adjust which values are set to x and y to see the solution space for those values, given your existing values. the solution space is where three of the areas overlap (one from each pair). one should note that at usually least one of the pairs will not depend on x or y, and therefore either cover the entire screen, or not exist. m is also just a buffer, because inequalities are not graphed when one side is undefined. The bigger m is, the larger the values the function is accurate for. (do not make m or m2 negative) it sets the number of turns to beat the opponent to m*opponent's Hp. also this is just for the three character situation (and I used my original three character solution to test it), I plan to make another for the four character one. I also think the second smaller inequalities might be contained in the larger ones, and therefore be irrelevant.
given the fact one always wins if they takes 0 damage, we can set up R with 1 defense, P with 2 attack and super low hp, S with 1 attack and super high hp
intended solution for ABCD:
given the fact that fight ties if both sides can't damage each other or both sides die in the same turn
we can set up A and C with high defense so that they can't hurt each other
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2 more difficulty ideas:
Medium Easy: set attributes for Rogue, Paladin, Shaman and Pay-to-win so that Pay-to-win wins all three, the rest win 1 and lose 2.
Medium Hard: set attributes for Rogue, Paladin, Shaman and All-rounder so that All-rounder ties all 3, the rest win 1, lose 1, and tie 1.
here is the abcd solution with variance:
https://www.desmos.com/calculator/ckngbupfif
type it in though, clicking the link does not work
unfortunately, four character solution requires all six colours demos has to offer.
https://www.desmos.com/calculator/qqyyxxb6iw
https://www.desmos.com/calculator/6vkfwoogbs
sorry, usage of m gave the victory to whoever had the higher hp when there was a stalemate.
I'm gonna solve it by graphing
https://www.desmos.com/calculator/iwncb9y1bs
Not the intended solution, but a really cool one. (That's what open-ended puzzle is about)
You can adjust which values are set to x and y to see the solution space for those values, given your existing values. the solution space is where three of the areas overlap (one from each pair). one should note that at usually least one of the pairs will not depend on x or y, and therefore either cover the entire screen, or not exist. m is also just a buffer, because inequalities are not graphed when one side is undefined. The bigger m is, the larger the values the function is accurate for. (do not make m or m2 negative) it sets the number of turns to beat the opponent to m*opponent's Hp. also this is just for the three character situation (and I used my original three character solution to test it), I plan to make another for the four character one. I also think the second smaller inequalities might be contained in the larger ones, and therefore be irrelevant.
There is an intended solution?
intended solution for RPS:
given the fact one always wins if they takes 0 damage, we can set up R with 1 defense, P with 2 attack and super low hp, S with 1 attack and super high hp
intended solution for ABCD:
given the fact that fight ties if both sides can't damage each other or both sides die in the same turn
we can set up A and C with high defense so that they can't hurt each other
B and D with low hp so that they otk each other
modify their stats to form a loop
I forgot the intended solution for ABCDE
ABCDE is similar to RPS, with two high hp heroes, two high defense heroes, one high attack hero, and more adjustment
my solution for RPS:
high hp for R, attack for S<(R hp)/2, defence for P>0 and <(S att)
I will use my equations to achieve the intended solution
this demonstrates how hard it is:
https://www.desmos.com/calculator/3rhphvwvip
big inequalities= turns to defeat opponent vs turns for opponent to defeat you
small inequalities asks do you block all your opponents attack while they don't block yours?
what is RPS?
rock paper scissor
It took me unbelievably long to notice it's RPS, ABCD and ABCDE.
I do think the second one is harder than the third.