Root chakra puzzle

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====== Root chakra puzzle ======
===[iron labyrinth module]===
~~TOC~~
//**This page contains spoilers for the Iron Labyrinth one-shot**//

The Iron Labyrinth has six puzzles for the players to solve. The Root chakra puzzle is the first puzzle that the players will encounter should they take the right-hand door from the starting positions

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==== Puzzle setup ====
When the players enter the room, it is mostly empty. There is a large root [[chakras|chakra symbol]] carved into the floor, which covers more than half the floor. In the center of the room are three scales made of metal. The scales have spherical shaped receptacles hanging on chains. On the "south" side of the room is a metal apparatus with a track that is similar in appearance to a bowling ball-return. On the wall above the apparatus is a riddle, carved into the wall

> One of these things is not like the others
> One of these bakers is not like the dozen
> Answer me this and win something bright,
> Which baker is heavy, or are they light?

On the "north" wall is a shelf attached to the wall, on top of which is a glass case that encloses a floating Garnet

Once the players have stepped into the room and observed it long enough to hear the description above, the apparatus has a "click" sound, and 13 stone balls a little smaller than a bowling ball roll out and fill the track of the apparatus, similar to the way it would look if a bowling ball return was full. The balls are numbered 1 through 13 with what looks like paint but is closer to a clay and rubs off if exposed to water

If the players attempt a fourth weighing, all balls not currently being bound to a players ki float out of the room. Shortly after this a new set of 13 balls is delivered to the players via the apparatus

The odd ball is always the ball marked 13. Each time a set of balls is delivered to the players, make a show of rolling 4d6 so that the players believe the result is always random. If the result of the roll is even, the 13th ball is heavy, if the roll is odd, the 13th ball is light. Fun fact, 4d6 can be used to simulate a 13 sided die

If the player tries a [[Recall Knowledge]] or [[Investigation#Deduction]] (Investigation) check and gets a 3 or higher, they remember/solve the standard solution and realize that with 13 balls and 3 measurements, they will always be able to find the odd ball, but may or may not know if the ball is heavier or lighter

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==== Normal solution ====
This problem is often posed as the 12 ball problem or the 8 ball problem, giving the players a set of balls and just enough uses of the scale to accomplish this. The solution involves figuring out the appropriate number of balls to weigh against each other such that you discover the odd ball. The solution is straightforward but has alot of moving parts, here is a link to an excellent write up of the [[http://www.mytechinterviews.com/12-identical-balls-problem|solution]].

As the question is worded, this puzzle is impossible without getting lucky. It would be possible to find the odd ball out of thirteen with three weighings if we only needed to identify the ball. Since the riddle requires whether the ball is heavier or lighter, we need more than three weighings

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==== Actual solution ====
There are a few ways the players can tackle this that i can think of:
  * They can solve the problem as if trying only to identify the odd ball and then force it to be heavier by using [[petramancer#Compact Earth]] to merge it with additional stone
  * They can solve the problem as if trying only to identify the odd ball and then force it heavier using [[desimancer#Resistance]] or lighter via [[desimancer#Impetus]]. For these solutions, the player needs to answer the question while the ability is active in order for it to be true
  * They could find the odd ball and then simply do some damage to it and call it lighter. This goes against the spirit of the puzzle


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==== Reward ====
The garnet inside the glass case has six facets and [[keystones#Luck]] 2. This grants 6 uses of advantage on skill checks, ability checks, or hit rolls. Alternatively you can opt to reroll 1's on a single roll
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