## Puzzle challenges!

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Ephraim
Posts: 47
Joined: July 3rd, 2017, 2:03 pm
Location: The Great Library of WML, Studiying it

### Puzzle challenges!

Hello everyone!

This topic is a recopilation of puzzles that will make you think a lot.

Rules:

The person who solved the last puzzle can post another puzzle. If he/she doesn't know any other one, he/she can just say «I don't know any other one», and then, any person can give one, but only the first posted after the solution of the last puzzle will be the official one to solve.

List of puzzles:

The nine braziers
The holy water
The 100 green-eyed dragons
The two sages and the evil king
The four races
The four witness
The poisoned wine
The impossible math riddle
The 100 tigers and the sheep
The two paths (variation: The two gates)
The old hermit
The hanging one
The elephant
The spy
The 100 coins
The 101 dwarves (variation: The hats again)
The balancing scale
The 20 bags of coins
The spider and the ant
The 20 pirates
The 7 races of Wesnoth
The 4 injured men
The nested riddle
The other impossible math riddle
The footpad, the mage and the lord
The fuses and the lighter
The pair of socks
The extra coin

Have fun!

The nine braziers:

You enter a room with 9 braziers arranged in a square (3 x 3), all of which are off except the center one, that it is on. In order to advance your path, you must light them all. But they are not normal braziers, since ...

- If you turn on one, the one in the center (every time I talk about «the one in the center» I mean the one that is in the center of the square, NOT in the center of the line) and the opposite one will turn on.

- If you turn one off the center and its opposite turn off too.

- If one that is already on has to be turned back on then it turns off.

- If one that is already turned off has to be turned off, it will turn on.

- If you turn on the center one, it turns on the right line and the top center one too.

- If you turn off the center one, those on the left line and the bottom center turn on.

As I said before, it is a complicated puzzle. If you found the answer, post it here using this method:

Code: Select all

``````I turn on the center brazier,
I turn on the middle-left brazier,
I turn off the center brazier,
I turn on the bottom right brazier,
...
(Note: This is just an example)
``````
Solution and Winner:
Last edited by Ephraim on July 22nd, 2018, 10:52 am, edited 32 times in total.
The Great Library of WML is huge and extense. I must find the book who will lead me to create a perfect campaign.
Future Project: History of Vindalf

Velensk
Multiplayer Contributor
Posts: 3979
Joined: January 24th, 2007, 12:56 am

### Re: A very difficult puzzle

Just to confirm, the rules are as follows:
-You can toggle any of the switches.
-If you toggle a switch that isn't in the center you also toggle the center and the opposite switch.
-The center is conditional, if you toggle it while it's on it toggles one set of 4 switches and if you toggle it while it's off it toggles those four switches opposite switch.

Assuming my understand is correctly, I'm fairly confident it's impossible. I sketched the matrix and I don't think there's any way to go from all 0s to all 1s or vice versa. I haven't spent a lot of time trying to solve it but that'd be my guess just looking at the math.
"There are two kinds of old men in the world. The kind who didn't go to war and who say that they should have lived fast died young and left a handsome corpse and the old men who did go to war and who say that there is no such thing as a handsome corpse."

Ephraim
Posts: 47
Joined: July 3rd, 2017, 2:03 pm
Location: The Great Library of WML, Studiying it

### Re: A very difficult puzzle

Yeah, you are right with the rules.
Last edited by Ephraim on August 9th, 2017, 9:35 am, edited 1 time in total.
The Great Library of WML is huge and extense. I must find the book who will lead me to create a perfect campaign.
Future Project: History of Vindalf

Samonella
Posts: 370
Joined: January 8th, 2016, 5:41 pm
Location: USA

### Re: A very difficult puzzle

I puzzled over it for a bit and didn't come up with anything. Had a good time though.
Velensk wrote:-If you toggle a switch that isn't in the center you also toggle the center and the opposite switch.
Just to be clear, "opposite" means this:

Code: Select all

``````1 0 0
0 1 0
0 0 1``````
as opposed to this:

Code: Select all

``````0 0 1
0 1 0
0 0 1``````
right?

Also, it's not something silly like walking to a different side of the square so "left" is different, is it?
The last few months have been nothing but one big, painful reminder that TIMTLTW.

Creator of Armory Mod, The Rising Underworld, and Voyage of a Drake: an RPG

Inky
Moderator
Posts: 516
Joined: September 22nd, 2014, 1:02 am
Location: USA

### Re: A very difficult puzzle

Samonella wrote:Also, it's not something silly like walking to a different side of the square so "left" is different, is it?
Ohh I like this solution, very creative! Or maybe, you could just pick up the braziers and rearrange them

If it's not something creative and "opposite" means the first matrix in Samonella's post, then it doesn't seem possible? Or I'm not interpreting it correctly?
Basically, the number of times you turn the center on should have the same parity as the number of times you turn it off, and the number of times you toggle each of the 4 opposite pairs should also have the same parity (opposite to the one above) so then there's an even total of operations but since every operation toggles the center there should be an odd number?

Elder2
Posts: 361
Joined: July 11th, 2015, 2:13 pm

### Re: A very difficult puzzle

Isn't there a feedback? If switching any brazier outside the center causes the center and the opposite one to switch on, then by the rules switching on the center (and it doesnt work only for the center, in fact if switching on any brazier causes the center and the opposite one to light on, well if we follow this logic it gets rather crazy) causes one side to light up, we can go further than that but the idea itself is silly.

So if we assume there is no feedback, which seems to be the only possible option, then, well if i understood it right then the sulution would be like this, surprisingly simple:

Code: Select all

``````I turn on middle
111
011
001

I turn off middle
011
101
110

I activate top left one or bottom right one
111
111
111``````
Did I get it right? This is a fun riddle

Inky
Moderator
Posts: 516
Joined: September 22nd, 2014, 1:02 am
Location: USA

### Re: A very difficult puzzle

ElderofZion wrote:I turn on middle
111
011
001
Ephraim wrote:- If you turn on the center one, it turns on the right line and the top center one too.
I think turning on the middle would actually be this?

Code: Select all

``````0 1 1
0 1 1
0 0 1``````

Ephraim
Posts: 47
Joined: July 3rd, 2017, 2:03 pm
Location: The Great Library of WML, Studiying it

### Re: A very difficult puzzle

Inky wrote:
ElderofZion wrote:I turn on middle
111
011
001
Ephraim wrote:- If you turn on the center one, it turns on the right line and the top center one too.
I think turning on the middle would actually be this?

Code: Select all

``````0 1 1
0 1 1
0 0 1``````
Yes, the top left brazier doesn't switch on, as Inky wrote. I have to say that... there isn't a solution. It can only be solved if the center brazier is turned on yet, at the start of the game.
But I want to make it difficult, because...

Code: Select all

``````0 0 0
0 1 0
0 0 0
I turn off the center brazier,
1 0 0
1 0 0
1 1 0
I turn on the center brazier.
1 1 1
1 1 1
1 1 1``````
It's too simple. Maybe, if we change the rules like...
If you turn off the center brazier, the left column and the bottom center ones turn off too.
What do you think about it?
The Great Library of WML is huge and extense. I must find the book who will lead me to create a perfect campaign.
Future Project: History of Vindalf

Ravana
Moderator
Posts: 1964
Joined: January 29th, 2012, 12:49 am
Location: Estonia
Contact:

### Re: A very difficult puzzle

As I told you in pm, with your original production rules

Code: Select all

``````{'101110010', '000001111', '011010110', '100100110', '000110111', '000101000', '
010100101', '001100011', '011110001', '111100000', '110110100', '110101011', '01
1101110', '101010101', '001000100', '111111111', '100011110', '111000111', '1001
11001', '011001001', '110001100', '010111010', '110010011', '001111100', '101001
010', '100000001', '010000010', '001011011', '010011101', '111011000', '00001000
0', '101101101'}``````
can be changed to 111111111. I just picked '000010000' for you as it has least already on.

I wrote nonrecursive DFS algorithm for this.

Ephraim
Posts: 47
Joined: July 3rd, 2017, 2:03 pm
Location: The Great Library of WML, Studiying it

### Re: A very difficult puzzle

Ravana wrote:As I told you in pm, with your original production rules

Code: Select all

``````{'101110010', '000001111', '011010110', '100100110', '000110111', '000101000', '
010100101', '001100011', '011110001', '111100000', '110110100', '110101011', '01
1101110', '101010101', '001000100', '111111111', '100011110', '111000111', '1001
11001', '011001001', '110001100', '010111010', '110010011', '001111100', '101001
010', '100000001', '010000010', '001011011', '010011101', '111011000', '00001000
0', '101101101'}``````
can be changed to 111111111. I just picked '000010000' for you as it has least already on.

I wrote nonrecursive DFS algorithm for this.
As I said before, this code says that the center brazier must be alredy on, and it's too easy to solve, then.
The solution is turn off the center one, and then, turn on the center one too.
The Great Library of WML is huge and extense. I must find the book who will lead me to create a perfect campaign.
Future Project: History of Vindalf

Ravana
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Posts: 1964
Joined: January 29th, 2012, 12:49 am
Location: Estonia
Contact:

### Re: A very difficult puzzle

That covers 2 of these 32. There are 30 other states that lead to solution.

Elder2
Posts: 361
Joined: July 11th, 2015, 2:13 pm

### Re: A very difficult puzzle

Well, I thought that by "the top center one" you mean top center line, though, now that I think about that it leads to feedback, but well, it seems that Ravana solved it.

Ephraim
Posts: 47
Joined: July 3rd, 2017, 2:03 pm
Location: The Great Library of WML, Studiying it

### Re: A very difficult puzzle

ElderofZion wrote:Well, I thought that by "the top center one" you mean top center line, though, now that I think about that it leads to feedback, but well, it seems that Ravana solved it.
I want to make this puzzle very difficult to solve, and that it hasn't got 32 possible answer. A puzzle that makes the person think a lot, but that has a solution. Someone knows how (changing the rules or something) make it more difficult?
The Great Library of WML is huge and extense. I must find the book who will lead me to create a perfect campaign.
Future Project: History of Vindalf

Ravana
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Posts: 1964
Joined: January 29th, 2012, 12:49 am
Location: Estonia
Contact:

### Re: A very difficult puzzle

If it is solvable, then by including symmetrical rule, you have infinite solutions by using that rule twice, however many times.

Inky
Moderator
Posts: 516
Joined: September 22nd, 2014, 1:02 am
Location: USA

### Re: A very difficult puzzle

Ephraim wrote:I want to make this puzzle very difficult to solve, and that it hasn't got 32 possible answer.
There are 32 starting configurations for which there exists a solution, not 32 different solutions for a given starting configuration.
Ephraim wrote: I have to say that... there isn't a solution.
Well, I liked my idea of rearranging the braziers yourself

I think there is a simple way to figure out valid configurations for the original problem:
math