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-   -   September 2020 (https://www.mersenneforum.org/showthread.php?t=25890)

tgan 2020-08-31 13:45

September 2020
 
[url]http://www.research.ibm.com/haifa/ponderthis/challenges/September2020.html[/url]

Till 2020-08-31 14:20

[QUOTE=tgan;555530][URL]http://www.research.ibm.com/haifa/ponderthis/challenges/September2020.html[/URL][/QUOTE]


[QUOTE] the permutation (0 2), which switches 0 and 2 but keeps 1 intact, results in the rules
[CODE]
2 -> 1
1 -> 0
0 -> 2 [/CODE][/QUOTE]
The challenge description is buggy, or not?

Dieter 2020-08-31 15:08

[QUOTE=Till;555535]The challenge description is buggy, or not?[/QUOTE]

I think so, too. If rps = 0,1,2, then 0 -> 1 would mean: rock beats paper. When I was a child, a rock was envelopped by paper...

virgo 2020-09-01 10:32

I guess its not buggy
description says "which are different ("Paper beats Rock"), so (0 2) is not an automorphism of RPS."
which means (0 2) is not automorphism of RPS(3)
fyi:I think permutation (012) is automorphism of RPS(3) because if you change 0 to 1, 1 to 2, 2 to 0, it keeps vertices and edges

btw, I can't still understand what "a0 b0 c0 d0" means..
what does alphabet at left hand side mean?

Dieter 2020-09-01 10:42

[QUOTE=virgo;555630]I guess its not buggy
description says "which are different ("Paper beats Rock"), so (0 2) is not an automorphism of RPS."
which means (0 2) is not automorphism of RPS(3)
fyi:I think permutation (012) is automorphism of RPS(3) because if you change 0 to 1, 1 to 2, 2 to 0, it keeps vertices and edges

btw, I can't still understand what "a0 b0 c0 d0" means..
what does alphabet at left hand side mean?[/QUOTE]

The solution shall be something like
0 -> 1,2,3,4
1 -> 2,3,4,5
.........
8 -> 0,1,2,3

Dieter 2020-09-01 10:54

[QUOTE=virgo;555630]I guess its not buggy
description says "which are different ("Paper beats Rock"), so (0 2) is not an automorphism of RPS."
which means (0 2) is not automorphism of RPS(3)
fyi:I think permutation (012) is automorphism of RPS(3) because if you change 0 to 1, 1 to 2, 2 to 0, it keeps vertices and edges

btw, I can't still understand what "a0 b0 c0 d0" means..
what does alphabet at left hand side mean?[/QUOTE]
The examples are unusual.
0 -> 1
1 -> 2
2 -> 0 with rps would mean
„rock beats paper and paper beats scissors and scissors beats rock.

Dieter 2020-09-01 11:05

[QUOTE=virgo;555630]I guess its not buggy
description says "which are different ("Paper beats Rock"), so (0 2) is not an automorphism of RPS."
which means (0 2) is not automorphism of RPS(3)
fyi:I think permutation (012) is automorphism of RPS(3) because if you change 0 to 1, 1 to 2, 2 to 0, it keeps vertices and edges

btw, I can't still understand what "a0 b0 c0 d0" means..
what does alphabet at left hand side mean?[/QUOTE]

The example

0 -> 1, 3
1 -> 2, 4
2 -> 0, 3
3 -> 1, 4
4 -> 0, 2

is consistent, and it has 5 automorphisms, but it isn‘t the usual „Rock-Paper-Scissors-Lizard-Spock" game.

The usual game is


0 -> 2, 3
1 -> 0, 4
2 -> 1, 3
3 -> 1, 4
4 -> 0, 2 (rock beats scissors and lizard and so on.
If that‘s wrong, please tell me!

uau 2020-09-01 15:27

[QUOTE=Dieter;555636]but it isn‘t the usual „Rock-Paper-Scissors-Lizard-Spock" game.[/QUOTE]

Isn't this just the same issue as with the first example, in that it doesn't seem to match the obvious assignment of numbers to names (rock=0, paper=1, scissors=2)? Both have "0 beats 1" while normally rock does not beat paper. But the structure of the game is the same, and if you swap the labels "0" and "2" then you get the standard rock-paper-scissors, and the 5-choice version matches what you gave too.

LaurV 2020-09-03 06:40

Formulation is not buggy, is just bad worded: "permutation blah blah is a permutation because blah blah". Of course is a permutation, but it should say "is an automorfism because blah blah"... And so on. The "math" is right.

The puzzle is not very difficult.

retina 2020-09-03 06:54

So this is just [url=https://en.wikipedia.org/wiki/Nontransitive_dice]nontransitive dice[/url] in disguise, right?

LaurV 2020-09-03 07:16

[QUOTE=retina;555860]So this is just [URL="https://en.wikipedia.org/wiki/Nontransitive_dice"]nontransitive dice[/URL] in disguise, right?[/QUOTE]
Game is the same. Puzzle is different.


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