So I had an idea for a number-based door puzzle that could readjust itself every time a wrong guess is made. Here’s the basic premise:

Given two numbers, find two more numbers in such a way that:

• no number differs from any other number in the same way,
• and none of these differences are part of the series themselves,
• and no number is bigger than it has to be, but not zero.

It seems fully deterministic to me, so let me give you an example:

Given are two numbers (1, 4). The difference is 3. 2 is out because its difference from 1 is part of the series, and in itself would be the difference from 4. 3 is out because of its difference from 2 and 4 being the same, and that difference would be 1, which is additionally part of the series. 5 is not valid either, but 6 is. 7 is not valid due to its difference to 6 being part of the series, and 8 is invalid because of the difference between (6, 8) and (4, 6). However, 9 is valid, and concludes the series.

It seems simple enough for a door puzzle, and given the above set of rules, it seems absolutely deterministic. I was considering to give the following (more vague) clue to its solution:

No siblings differ alike, nor match they their differences, and none grow taller than they must.

I need it to sound like a riddle, but still be concise and accurate and its description of the puzzle. If anyone has any suggestions, I would greatly appreciate the help.

I suppose I have four questions for this community:

• Is there a unique solution for any two starting numbers below 10?
• Can you think of a more interesting variant, like perhaps by minimising the sum of the numbers (but not having any predetermined numbers given – (1, 4, 6, 9) being the best solution I found so far)?
• It seems to me there should be some way to determine the two missing numbers in a way that minimizes the sum of all four, which is not the same as choosing the lowest possible numbers one after the other. Is there such a way?
• Is there a better way to phrase the problem in a single sentence to my players, without being too obvious or sounding too scientific?

And some more example solutions for your convenience:

• (3, 4) –> (9, 11)
• (2, 5) –> (6, 13)
• (1, 9) –> (3, 13)
• (1, 3) –> (7, 12)
• (1, 5) –> (7, 13)
• (4, 6) –> (1, 13)
• (8, 1) –> (3, 17)
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## Aztec/Mayan Temple Guardian monster, puzzle, and encounter ideas? [closed]

In a few weeks, I’m running a 10th level DnD 5e Indiana Jones-esque one-shot type jungle adventure in my homebrew world. My players are fighting golems, dinosaurs, etc. But I’m struggling to design a cool and engaging encounter when they finally reach the top of the ruined pyramid they’re going to explore. The pyramid was built by sun-worshipping natives that had a strange connection with extraplanar and alien beings. What kind of monsters do you think would be interesting and cool to be guarding this place at the top of the pyramid? I’m also planning to make this puzzle were they have to figure out a way to open a circular pressure plate at the center of the chamber at the top of the pyramid to enter as well, and would like to hear your suggestions or ideas on how I could execute this?

I’m open to all suggestions!

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## solving algebraic puzzle using the mathematica

I have tried to solve this algebraic puzzle,

$$abc+abc+abc=ccc$$

using mathematics but I don’t know what I am doing wrong. Can you help me?

I have tried these three ways

$$Reduce[3 (100 a + 10 b + c) == 100 c + 10 c + c, 0 <= a <= 9, 0 <= b <= 9, 0 <= c <= 9, Integers]$$

$$Solve[3 (100 a + 10 b + c) == 100 c + 10 c + c, 0 <= a <= 9, 0 <= b <= 9, 0 <= c <= 9, Integers]$$

$$FindIntance[3 (100 a + 10 b + c) == 100 c + 10 c + c, 0 <= a <= 9, 0 <= b <= 9, 0 <= c <= 9, Integers]$$

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## Is a puzzle box considered locked?

As part of some treasure the party I am in found, we found a puzzle box. I am a wizard, and I wanted to use the spell Knock to open it. Knock says:

Choose an object that you can see within range. The object can be a door, a box, a chest, a set of Manacles, a padlock, or another object that contains a mundane or magical means that prevents access.

A target that is held shut by a mundane lock or that is stuck or barred becomes unlocked, unstuck, or unbarred. If the object has multiple locks, only one of them is unlocked.

(emphasis mine). None of my party rolled high enough on an Investigation check to manage to open the box, and I said I wanted to cast Knock to open it. My rationale was that each step of the puzzle was a lock, and if I casted Knock enough times, it would open the puzzle box.

However, my DM said that the puzzle box isn’t technically “locked”. My thought was that since Knock will unstick or unbar doors, the item doesn’t need to be technically locked with a physical lock, it just needs to prevent us from opening it. I did not want to fight about it, so I dropped it, but I was curious if there is an official ruling. However, I did read this post and I’m not sure if the top answer agrees or disagrees with my specific situation.

So, can Knock open a puzzle box? If so, would it take one casting total, or one casting for each step of the puzzle?

## 8*8 slide puzzle using hill climbing local search AI technique

can we solve an 8*8 slide puzzle using random-restart hill climbing technique (Steepest-Ascent)? if yes how much computing power will this need ? and what is the maximum n*n that can be solved normally? say with a google colab instance

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## Grid Puzzle Split Algorithm

What could be the best approach to divide an $$N\times N$$ grid into $$N$$ groups having $$N$$ tiles each? Is there a well-known algorithm to create a random puzzle of this type? I could not find a direct answer on the net. Max grid size will be 10×10. Below is an example for 5×5 grid. ## A state space for river crossing puzzle

I am solving the river crossing puzzle with 6 participants. You must transfer all the people across the river in this flash game respecting the following rules:

The ferry can carry no more than 2 people. Only the Adults (mom, dad and policeman) can operate the ferry. Dad can not be in the presence of the girls w/out Mom Mom can not be in the presence of the boys w/out Dad The thief can not be alone with any of the family w/out the policeman.

We need to create the state space and as I am creating mine I am not sure if I am doing it properly.

In my case I represent the state as A/B where A are the people on the left side and B are the people on the right side. This is what I have so far. I feel like I will get a lot of states, so I am worried that I am doing something wrong. Is this correct? ## Can the KenKen puzzle be solved using the same ideas as for Sudoku?

There are many ways of solving Sudoku puzzles, however two good approaches are the Algorithm X and solving using Linear programming. Is it possible to solve the KenKen puzzle using Algorithm X (turning the problem into an exact cover problem) or using Linear programming and how could that be done if possible?

## NP-completeness of crossword puzzle

How to prove that this crossword puzzle is NP-complete?

• We have an instance of crosswords in a square grid $$G$$ ​​of size $$m \times m$$.

• We have a set of black boxes $$N$$.

• We have a dictionary of words $$D \subseteq\Sigma$$, where $$\Sigma$$ is a finite alphabet.

The question is whether there is a way to fill in the white boxes ($$G\setminus N$$) so that all the horizontal and vertical words belong to $$D$$. Here we suppose $$|\Sigma|\geq 3$$.

Also note that the reduction should not create a dictionary that is too large.

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## How can I get a patent/Copyright for the puzzle game I invented?

I have invented a new puzzle game which I have able to play on paper.

However, I want to create a mobile app/web app to let other users play like other below games.

Example: Threes, 2048

But being not a good UI developer myself, I was thinking to contact other UI developer. But if I tell the idea behind my game to them, they could ignore me and launch the game themselves.

How can i get copyright access for the puzzle game I invented?

If the platform for asking this question is wrong, kindly tell me where I can ask this question.

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