# Help! I Need a logic puzzle in two hours!



## Remathilis (Jun 3, 2005)

Ok, the scenario.

I have a Star Wars game where a group of jedi are going into an abandoned jedi temple once full of prophets. They have a holocron, but to get to it, they need to pass three trials. I need a logic puzzle that the players can solve to advance through the trials. 

My original idea was something akin to mindsweeper, but I'm open for anything. Remember, you have to make due with technology and some force-mystical abilities, not regular D&D magic. Adapted puzzles, links, anything is fine, as long as I have a solution for it. 

And no, I don't want the Puzzle-from-Hell (TM) that was posted a few weeks back. 

Thanks.


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## BiggusGeekus (Jun 3, 2005)

Pulled this from a google search, there are others on the site

http://perplexus.info/show.php?pid=3132&op=sol



> In the Eternal Forest, the trees are perfectly circular, each having a diameter of exactly one meter. They are arranged in a flat, infinite rectangular grid. The center of each tree is ten meters away from the centers of each of its closest neighbors.
> There are many paths through the Eternal Forest. Each path is infinite in length, constant in width, and perfectly straight. Trees don't grow on the paths, but every path will have tree trunks touching it on either side.
> 
> What is the narrowest possible path through the Eternal Forest?




[spoil]
	
	



```
10/sqrt(97) - 1, or about .0153461651 meters. This path has a slope of 4/9.
Every path is parallel to a set of lines that go through the centers of trees. Paths with irrational slopes will eventually hit a tree.

A set of parallel lines with the slope p/q (where p and q share no factors) can be described with the equation px-qy=10c, where c is a different integer for each line. To determine the width of a path parallel to these lines, we must determine the distance between each line. This distance can be determined by finding the altitude of a certain right triangle much like the one drawn below.


   /   /|  /
  /   / | /
 /   /  |/
/   /___|
   /   / 
This right triangle is constructed by first drawing the line in the set that goes through a tree's center at the origin. This line has the equation px-qy=0. The next closest line has the equation px-qy=10. Using any tree on the latter line as the right angle, and the former line as the hypotenuse, we draw a right triangle with horizontal and vertical legs.
If the slope of the lines is p/q (in lowest terms), then the vertical leg of the triangle is 10/q and the horizontal leg is 10/p. The altitude is 10/sqrt(p² + q²), but the width of the associated path is one meter less than that, because of the radii of the trees.

Therefore, the width of any possible path through the Eternal Forest can be described as 10/sqrt(n) - 1 meters, where n is the sum of the squares of a pair of relatively prime numbers.
```

[/spoil]


I would personally beat you with a mallet if you gave this to one of my characters, but hey, there was time pressure.


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## BiggusGeekus (Jun 3, 2005)

Here's another:



> What are the next two numbers in this sequence:
> 1, 2, 4, 16, 26, 42, 57, 512, 730, 1010, 1343, 1872, 2367, 2954





```
3616, 65536 
Express the nth number in base n:

1  1     1
2  2     10
3  4     11
4  16    100
5  26    101
6  42    110
7  57    111
8  512   1000
9  730   1001
10 1010  1010
11 1343  1011
12 1872  1100
13 2367  1101
14 2954  1110

Continuing the pattern:
15 3616  1111
16 65536 10000
```


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## Storyteller01 (Jun 3, 2005)

Found this one in FFG's "Traps & Treachery":

In front of the players is an iron door with no obvious methods of entry (matter of fact, it's completley smooth). ABove the door are eight identically cut crystals. Above the crystals is a message: Music is the key ( of course, the message is purely optional    ).

If anyone approaches the door, the crystals glow and give a clear musical tone in a specific order (all crystals are counted from the left side):

1) Fourth 
2) Sixth
3) Eighth
4) Sixth
5) Second
6) Third

The crystals represent a musical octave (c, d, e, f, g, a, b, c)

The tones spell the word 'facade'. The door is actually an illusion covering a wall of force (so knock doesn't work). When the password is spoken (facade), the illusion and the wall disappear.


You can do the same with your campaign, replacing the illusion and wall with a forcefield and hologram. It would be even cooler if you can a musical instrument to play the notes with (you might find something on-line if your computer has speakers)!

The book recommends using a Perform check (DC: 12) to recognize the octave, then letting the players put it together from there.


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## Storyteller01 (Jun 3, 2005)

Here's another. if your feeling evil:

In front of the players is a statue with its arms extended in front, palms up. Close inspection of the statue shows that the arms are actually a form of balance. In front of the statue are eight slim steel dicks (the weights of Authority and Responsibility). 

The following is engraved at the base of the statute:


"_You face the weights of authority and resposibility. Balance them well, lewst you sow disaster. Balance them and you shall open the path.
_

_It will help you to know that the first is ten times the second._ (weight 1: 130)

_Thrice the second is the third plus twice the eighth._ (weight 2: 13)

_Twice the third is one more than the fifth plus half the eight_. (weight 3: 7)

_The fourth is the difference between the sixth and twice the second_. (weight 4: 44)

_The fifth is one tenth of the sum of thrice the second and one fourth the fourth._
(weight 5: 5)

_The sixth is the first minus twice the third plus twice the fifth._ (weight 6: 126)

_The seventh is the difference between four times the fourth and the sum of the first and the fifth_. (weight 7: 41)

_Twice the eighth is one less than twice the second plus the third._ (weight 8: 16)"


If the balance is off by less than 4 ounces, nothing happens. If it is off by more than four ounces a trap is sprung (a different one for each arm, you pick what you want  ).


To be truely evil, make it so that only those with telekinesis can reach the discs (if you have jedi).


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## WinnipegDragon (Jun 3, 2005)

This one stumped my party for a loooong time:

There is a series of cups organized in rows, in which are a number of pebbles.  Each cup contains one or more pebbles.  The pattern goes as follows:

1
11
21
1211
111221
312211
13112221

The last row of cups is empty.  There are ten cups.  How many pebbles are placed in each cup?

The answer is:

1113213211

The secret is that each row of cups describes the row above it.  The first row contains one one.   The next row contains two ones.  The third row is one two, then two ones, etc...

It's an evil stumper of a puzzle!


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## RangerWickett (Jun 3, 2005)

For Jedi, how about a trial that teaches them not to take things at face value:

The classic "One of us lies, one of us tells the truth" riddle.

There are two doors, sealed, with a stylized hologram of a face floating in front of each. Each door is equipped with two blaster turrets, and they sit motionless until someone comes within 10 feet of either door, then they activate and track the person. They don't fire unless the person actually tries to tamper with the doors.

As soon as the Jedi enter the room, a hologram in the center of the room flickers on, scrolling out the following:

"One of these doors leads to death, one continues on to the prize you seek. You may ask one door's hologram one question, but be warned: one tells only the truth, and one tells only lies. Ask the right question, and you will know which path is safe. Once you make your choice, the other way will be barred to you. If you are in a group, one choice affects all the group."

A casual investigation from across the room reveals that each door seems to be equipped with a disintegration gun, so they can guess that if they choose wrong, they'll die. If they try to force their way through one of the doors or dismantle the disintegration gun, the turrets fire at them and the hologram faces snarl angrily.  It's possible to fight your way through, though. In fact, that's the real solution.

You see, in a normal logic puzzle like this, you ask one door, "What would the other door say if I asked it if the left door is safe?"  

If the left door is safe, regardless of who you ask, you'll get the answer, "The left door is unsafe."  This is because if you ask the truth teller, he'll tell you the other door's lie, and if you ask the liar, he'll lie about what the truth teller would say.

If the left door is unsafe, regardless of who you ask, you'll get the answer, "The left door is safe."

But here's the kicker.  _Why the hell are you trusting a pair of talking doors in a place like this?_ The doors are both fully capable of lying or telling the truth. Regardless of what question the party asks, they'll give an answer like, "The left door is safe."  Then, when they try to go through that door, the disintegration gun shoots them, doing lots of damage if they're not fast.

After the smoke clears from the inevitable battle to follow, the hologram in the center of the room changes and says, "I lied. No question was the right one to ask. The lesson is that sometimes your foes will try to deceive you. If you have survived, though, you must not be completely incompetent, so you can pass."

For extra fun, pump deadly gas into the room, and require an emergency Computer Use check to open the doors and get the party out before they're poisoned.


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## RangerWickett (Jun 3, 2005)

(From Harry Potter book I, never made it into the movie.)

You enter a room in a dungeon, and suddenly the exits ahead and behind are shrouded with flames. Their heat is intense, and your meager elemental wards will not protect you if you try to leap through them. You know a villain has already passed this way, and if you fail to follow him, he will recover a powerful and dangerous magic item, so you dare not turn back.

The only clues in the room are a rack of seven different vials, and a scroll with a riddle. The image below gives you the necessary information. Which vial do you choose?


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## Mark (Jun 3, 2005)

There something in this free adventure that might be useful to you -

http://www.rpgnow.com/product_info.php?cPath=268&products_id=4496&src=enworld

Did I mention it was free?


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## ender_wiggin (Jun 4, 2005)

I learned this puzzle when someone on Enworld posted it (forgive me, I've forgotten who).

"Five pirates, of varying rank, come across a treasure chest with a thousand pearls in it...

...the code states that the protocol of the division of treasure is this:

The lowest ranked pirate proposes a plan for dividing the treasure. The other pirates vote on the plan -- if it passes (by at least a 50% vote) the plan goes into effect. If the plan does not pass, whoever suggested the plan is killed, and the next lowest ranked pirate proposes _his_ plan.

Now, assuming all the pirates are very greedy and very smart...

...how many pirates were killed, and of the remaining pirates, how many pearls did each get?"

THis puzzle can easily be converted to a SW setting: marauders and credits...


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## Olgar Shiverstone (Jun 4, 2005)

Two moldy oldies, since it's too late (extra points for those who recognize the original D&D appearance of these puzzles):

Complete this sequence to pass through a secret door:

O,T,T,F,F,S,S,E,_

Answer: 



Spoiler



N.  One, Two, Three, ...



Or,

Five Protocol Droids with blasters stand in a row, each with a number painted on his chest: 3, 5, 7, 9, 11.  When approached, all speak in unison: "One of us is not like the others.  Choose the one, and it will serve you.  Choose wrongly, and you will die." (If the players choose the wrong droid, all attack).

Asnwer: 



Spoiler



9.  The other numbers are primes.


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## John Cooper (Jun 4, 2005)

> Five Protocol Droids with blasters stand in a row, each with a number painted on his chest: 3, 5, 7, 9, 11. When approached, all speak in unison: "One of us is not like the others. Choose the one, and it will serve you. Choose wrongly, and you will die." (If the players choose the wrong droid, all attack).



Alternate (and equally correct, in my mind) answers:  



Spoiler



11, because it's the only 2-digit number.  

11, because it's the only number which, when written out, starts with a vowel.  

5, because it's the only number which, when written out, doesn't have two or more of the same letter (EE in 3 and 7, NN in 9, EEE in 11.)

3, because it's the only number, which, when written out, doesn't fit the alternating consonant/vowel pattern.

5, because it's the only number that has a single-letter Roman numeral equivalent.


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## Mark (Jun 4, 2005)

Olgar Shiverstone said:
			
		

> Five Protocol Droids with blasters stand in a row, each with a number painted on his chest: 3, 5, 7, 9, 11.  When approached, all speak in unison: "One of us is not like the others.  Choose the one, and it will serve you.  Choose wrongly, and you will die." (If the players choose the wrong droid, all attack).
> 
> Asnwer:
> 
> ...







			
				John Cooper said:
			
		

> Alternate (and equally correct, in my mind) answers:
> 
> 
> 
> ...





And therefore: 



Spoiler



7 because it is the only one for which a truly legitimate answer cannot be proffered?


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## Patryn of Elvenshae (Jun 4, 2005)

Poor 7.  Not even a possible answer!  

EDIT:

Mark's got the much better answer to that one ...


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## Mark (Jun 4, 2005)

Patryn of Elvenshae said:
			
		

> Poor 7.  Not even a possible answer!
> 
> EDIT:
> 
> Mark's got the much better answer to that one ...





_It's funny cause it's true..._ - Homer Simpson


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## Storyteller01 (Jun 4, 2005)

So, Remathallis, how did the game go?


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## Remathilis (Jun 5, 2005)

I used RangerWicket's puzzle...

I did manage to get out of the room before the players caught me B.A. Style...

Thanks all.


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## RangerWickett (Jun 5, 2005)

Victory!


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## Verequus (Jun 5, 2005)

ender_wiggin said:
			
		

> I learned this puzzle when someone on Enworld posted it (forgive me, I've forgotten who).
> 
> "Five pirates, of varying rank, come across a treasure chest with a thousand pearls in it...
> 
> ...




And what is the answer to this riddle?


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## ender_wiggin (Jun 5, 2005)

No pirates were killed. 

The least ranked pirate suggested this, which was accepted by 50% vote (1 and 3 accepted, 2 and 4 vetoed):

5th pirate (the one proposing the plan) gets 997 pearls.

3rd pirate gets 1 pearl.

1st pirate gets 2.

NOTE: you can replace 1st pirate with 2nd pirate and the solution still works

Explanation: Use recursive thinking.

If there's only 1 pirate left, he obviously gets all the money. 1000.

If there's two pirates left, the 1st pirate vetoes whatever the second pirate suggests. So we have 0/1000.

If there's three pirates left, the second pirate *must* accept, or else he dies. Thus, the third pirate will suggest that all the pearls goes to himself. So we have 1000/0/0

If there's four pirates, the third pirate will veto no matter what, knowing he will get all of it if the plan doesn't pass. Thus, he *can't* be bought. The other two, however, *can* be bought with 1 pearl each. Thus, we have 998/0/1/1.

If there's five pirates, the fourth pirate will veto unless you give him more than 998, because that's how many he  gets if the fifth's plan doesn't pass. But of course, the fifth pirate knows he can get away with more than that. One and two know they will each get 1 pearl if the plan doesn't pass, so if you give either of them more than 1 pearl, they will accept. Take your pick of 1 and two and bribe w/ two pearls. The third pirate knows he gets *nothing* if the fifth pirate's plan doesn't pass, so he only takes 1 pearl to bribe. Thus, with five pirates the solution is 997/0/1/0/2 OR 997/0/1/2/0.


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## Altamont Ravenard (Jun 5, 2005)

ender_wiggin said:
			
		

> No pirates were killed. [...]




Jesus... I can hear the moan of discouragment of a thousand players...

AR


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## Gez (Jun 5, 2005)

Here's a puzzle I like.


*From one, cut in four, and make two.*
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ 
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■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ​
The solution? First, I'll give you another example that works, too.


*From one, cut in four, and make two.*
■ ■ ■ ■ ■
■ ■ ■ ■ ■
■ ■ ■ ■ ■
■ ■ ■ ■ ■
■ ■ ■ ■ ■​
Still don't get it?
[sblock]OK, you have one square, you must cut it in four parts, and from these four parts, you must make two squares.
Hint 1: 



Spoiler



Think triangles.


Hint 2: 



Spoiler



Think triangles and squares.


Hint 3: 



Spoiler



Think Pythagoras' theorem.


Hint 4: 



Spoiler



It tells you when the area of one square is equal to the sum of the areas of two other squares.


Hint 5: 



Spoiler



For our example with the 17-unit square, you can get a 8-unit square and a 15-unit square, for 17²=8²+15². For the simpler example with a 5-unit square, 5²=3²+4².



OK, here are the solutions.
[sblock]
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
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■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

You have your 8-unit square (the red one), and with the other elements, you can get:
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
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■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

Likewise, for the smaller square:
■ ■ ■ ■ ■ ... ■ ■ ■ ■ ... ■ ■ ■
■ ■ ■ ■ ■ ... ■ ■ ■ ■ ... ■ ■ ■
■ ■ ■ ■ ■ ... ■ ■ ■ ■ ... ■ ■ ■
■ ■ ■ ■ ■ ... ■ ■ ■ ■
■ ■ ■ ■ ■
[/sblock]
[/sblock]


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## diaglo (Jun 7, 2005)

Olgar Shiverstone said:
			
		

> Two moldy oldies, since it's too late (extra points for those who recognize the original D&D appearance of these puzzles):...
> Five Protocol Droids with blasters stand in a row, each with a number painted on his chest: 3, 5, 7, 9, 11.  When approached, all speak in unison: "One of us is not like the others.  Choose the one, and it will serve you.  Choose wrongly, and you will die." (If the players choose the wrong droid, all attack).




that's not exactly the way they were presented in S2.    Dr. Frankenstein.


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