Four 5s (A Puzzle Dungeon)

Background

The Trigomancers, as they are now known, where an ancient race of dwarves who developed a understanding of mathematics, logic and engineering while most other races were still sleeping under skins and in un-worked caves. The Trigomancer’s civilization collapsed and disappeared suddenly prior to any historical chronicle. They are known to the contemporary races only through the ruins they left behind. But these ruins, an unfair title, are monuments to an ineffable civilization. The Trigomancers constructed enormous mountain halls, often changing the entire face of the mountain with fantastically engraved facades and elaborate entrances. Their mines were deep and their tunnel systems so extensive that they still haven’t fully been explored. Their writings, which adorn the walls of all their structures describe a complex economy, a well defined social strata, and a philosophy which intertwined mathematics, logic, arcane manipulations and disdain for divine powers.

The Trigomancers, like modern dwarves pursued riches beneath the earth. By many measures their mines were productive beyond modern standards however, when uncovered these ancient mines most often have stockpiles of rough gems and ores that the Trigomancers never processed. Indeed the Trigomancers mine shaft often have exposed yet un-worked veins of ore or gems. The most productive mines today are built on the sites of old Trigomancer mountain halls.

But these mines were not exploited without a cost. Trigomancers mines are built with elaborate trap that combine arcane talents, puckish engineering, and reverence for logic and numbers. The traps were designed to be easily accessible by adherents to the Trigomancy philosophy, but deadly to the blunt or uneducated. Deadly and well constructed, these traps kept the Trigomancer’s mines went unmolested for millennia. However the challenges are not insurmountable, skill engineers, studied sages and clever thieves have long since elucidated all the puzzles of the known Trigomancer mountain halls. Yet rumors still persist of yet undiscovered halls that hold untapped riches, for those brave enough to tackle the Trigomancer’s challenge.

Level 1: The entrance

The PCs are confronted with decorated façade of a large mountain hall. Like the city of Petra, columns and arches have been carved from solid rock. The walls also hold engraved images depicting the founding of the mountain hall and its construction. The mural clearly shows the dwarves finding gems and precious metals at this site. There are two large doors leading to hallway wide enough for double ox carts to move down side by side. The doors are shattered and the hallway in ruins. I envisioned this being placed in glacier, and the hallway being filled with ice, maybe the corpse of a mammoth type animal. At any rate as the PCs move down the hall they encounter and likely spring a trap. But the trap is damaged and doesn’t fire correctly. They encounter remains of mechanism, which at closer inspection controlled the trap. The device had five triggers, pulling of the correct trigger would disarm the trap, and pulling any other trigger would set off the trap. On the wall behind the ruined gearbox is some writing largely illegible now, that appeared to have been a riddle. The solution to the riddle indicates. When I ran this, I did have it in glacier, and I had the ruined trap be a water trap, and when the pipes froze they burst and destroyed the mechanism. The point of this scene is only that the PCs

A) PC sees that the builders of this dungeon-constructed complex puzzle triggered traps

B) There is likely to be wealth in these ruins

C) It is unlikely that the builders of this mountain hall are still here.

Level 2: Puzzle of 5 Weights

At the end of the tunnel the PCs see arched passageway leading to another room. Inside the room is glowing blue light and on the left side of the arch are the following numbers

64 81 100 121 144 169 196 225

On the right side of the arch are the following numbers

27 64 125 216 343 512 729.

Upon entering the room, the PCs will see 4 walls a floor and a ceiling. The ceiling decreases in height stepwise, with the highest area being at the archway and the lowest ceiling being opposite the archway.

The Blue Glow: The Blue Glow is plaque set in the middle of the room with glowing blue writing and glowing holy seal placed on it. The plaque was written by The Priests of Droven charged with surveying and mapping this area. The plaque reads, “

Greeting Brothers, Thanks be to Droven that my maps have lead you to this wonderful find. This is an undisturbed Trigomancer Mountainhall. As I am sure you have observed the outer hall has been ruined by nature but I believe that this room is entrance to a greater mine complex. Before you is an excellent example of a Trigomancer puzzle, and during my inspection it was in good working order and needed only to be solved in order to open the next door. Briefly the puzzle works as follows, on the right hand wall there are five coffers each marked with the name of a Trigomancer scared elements and each having unique key on it. The coffers are to be hooked to the chains. As you can see two off the coffers are flat pallets and three are buckets. To solve the puzzle you must place the correct amount of weight into each coffer and pull the release pin on the left wall. The basic Trigomancer unit of weight was simply called a unit. As you see on the right wall there are 125 blocks, each exactly the same and each weighing one unit. On the left wall you will note a spigot. This spigot dispenses thick oily liquid, one pint of which weighs one unit. When I left there was also a measuring cup on a shelf by the spigot, which holds exactly one Trigomancer pint. Each coffer weighs ten units and is we know Trigomancer accounting always included the weight of the container in calculations. Though we made full inspection of the device, we did not solve the puzzle my brothers, I leave that joy to you. Be of Use, Gild Inkangle, 578 (this date is over 200 years old)

Far Wall: Opposite the archway there are fives sets of three chains extending from the ceiling to the floor. The chains come out of openings in the ceiling and go into openings on the floor. Each set of three chains is arranged in a trianglular configuration with two chains closer to the archway and one chain farther back. Halfway between the floor and the ceiling there is hook attached to each chain. On the vertical plane of the stepwise ceiling directly above each group of chains is a word, from left to right the words are Arronite, Bosidian, Cantor, Dram and Ether. In between the chains on the floor of the Arronite, Bosidian and Cantor cluster is metal disc implanted in the stone floor and in the center of the metal disc female receptor similar to key hole, each one is unique. On the ceiling of the Dram and Ether clusters are also metal disc flush with the stone ceiling that have unique receptors. If the rains are tugged it is noted that they will move up and down. Arronite and Ether are connected, so when an Arronite chain moves up an Ether chain moves down. The chain can no farther than the hooks. Bosidian and Dram are also connected to so when Bosidian chains are fed downwards, Dram chains moves upward. The Cantor chains seem to move freely, but again no farther than the hooks.

Right Wall: The right contains stone shelves build into the rock. The stone shelves contain 125 blocks, two beat up but polished silver pallets and beat up but polished three silver buckets: these are the coffers. All of them have rings on them so they can be attached to chains. The two pallets are identical except for different keys on the bottom and different inscription. One pallet reads

Arronite must receive (illegible)

The other reads

Bosidian must receive (largely illegible but greater than 30)

One bucket says Cantor, it can hold 159 pints, and it has key on the bottom the other two buckets have keys on the upper lips. Dram can also hold 159 pints and the inscription on the Dram bucket read

You must place (illegible) units into Dram.

The Ether bucket is smaller it could only hold a max of 29 pints. Its inscription reads

(Illegible) units into Ether.

Left Wall: The left wall has a spigot and small shelf extending from the center of the wall. On the shelf is a polished sliver cup. The spigot dispenses an oily foul smelling liquid. Above the Spigot is writing in an ancient language (that the PC should be able to read).

The balance must be maintained as described in the ancient numbers.

Each weight is unique.

All weights greater than 40 must be perfect squares

All weights less than 40 must be perfect cubes

The weights are the total of the sacred coffers and the offerings.

To the left and right of the spigot the stone of the wall seems different, not like it is part of the natural rock. There are scratches on the floor in front this odd stone. These segments of stone radiate magic. They are golems, if the wrong combination is enters the stone will come alive, taking the shape of a large man. They will kill or chase off all the people in the room, then clean the room before returning to their places in the wall. In the bottom left corner of the left wall is a leaver. It is a position tagged Rest, it can be moved into a position tagged Weigh.

Entrance Wall/Archway wall: To the left of the archway is a pile of body parts. Mostly Orcs that have been ripped limb from limb and then stacked neatly in a pile. They sit frozen, and perfectly preserved. They were frozen before they were stacked but ripped limb from limb while alive, their bones often crushed. Within the pile of remains is a limbed torso of another being, perhaps a drow, but any intelligent being with a moral and cultural stance refractory to those held by the PCs will work. The Torso has a small book clutched in its hands. The book is a travel log telling the story of the bearer’s journey to this location. The primary emphasis is on mapping navigational information. The last entry of the log is splashed with blood reads as follows.

It is the Orcs' fault. The puzzle was easy. But I had to rely on the Orcs, because I could only lift the Cantor and Ether coffers once filled. The other three were too heavy but I knew the value they used for Bosidian was wrong, because they loaded an odd number of blocks. But they screamed at me, claiming they were right. And I pulled the pin anyway out spite. I did not know a wrong combination would release four go

The Lock: If somebody of skills inspects the locking mechanism they will realize that each keyhole has three triggers. The triggers are fired once the leaver has been moved to Weigh and the right weight and the right key are inserted into the lock.

A: 1 no matter the weight, 2 only if E 1 is also engaged then always, 3 is fired by unique weight, excludes 1

B: 1 no matter the weight, 3 only if D2 is engaged, and 2 fired by unique weight excludes 1

C: 2 no matter the weight, 3 uniquely with high pressure, 1 uniquely with moderate pressure excludes 2

D: 1 no matter the weight, 2 only if B3 is engaged, 3 uniquely

E: 3 no matter the weight, 1 only if A2 is also fired and 2 is fired with unique weight and it excludes 3

Level 3: The Enigma of divine taxes

After they solve the first puzzle, a ramp in the floor will lower and the PCs can go into the mines. The PCs can wander around the dungeon, I had some monsters and maze here. The only important thing is they learn is the Trigomancer year 15 months. They then reach the next puzzle. The PCs reach an apparent dead end of tunnel with a silver bucket hanging from the ceiling and a trough along the wall holding identical stone discs (like checkers). There is writing on the wall, which reads

Place 1 stone in the bucket for each talent paid by Cathagram, and then pull the leaver to gain access.

On the opposite wall is written.

The Story of Cathagram

Cathagram, Belagum and Dolivito were all patrons of the Lord Eustal. Every other month they each paid a tribute to the lord in the way of 5 talents. Rather than travel to Eustal they would each give Eustal’s servant Frogal 5 talents. On the first month of the year, Frogal brought the 5 talents directing after Eustal had a terrible dream. Eustal dreamed that the Gods judged him too greedy. So he commanded Frogal to take 1/3 of the tribute and return it to Cathagram, Belagum and Dolivito. Frogal being poor with number of poor morals decided to give Cathagram, Belagum, and Dolivito only 1 talent each, thus each made a tribute of only 4 talents. Frogal kept the other two talents. Sometime later Cathagram was traveling to distant land and bragged that he paid 12 talents to his lord in tribute. Word of this boast got back to Belagum and Dolivito, and they went to confront Frogal.

The demanded that Frogal publicly declare that each of the patrons had paid 4 talents. Frogal was confused, and frightened. In this panicked state he publicly declared not only that each patron had paid 4 talents, but that he had also kept. Eustal heard this and believed a miracle had happened. If he patron paid 4 talents (4 x 3=12) and Frogal had kept 2, then 12+2=14. What had happened to the 15th talent?

Eustal declared these divine taxes, and the ritual was repeated every other month. The 3 patrons would pay 5 talents each to Frogal, would take this to the Eustal, Eustal would give Frogal 5, he would return 3 and keep 2. After 20 years of this, Cathagram said he would pay Eustal the sum of all the divine taxes over the past 20 years all at once, if would have to make no more tribute. Eustal agreed. Starting with the first divine tax on the first month of 15-month year, and continuing every other month for 20 years, what was the sum of the divine taxes?

Solution: The answer is zero. Eustal’s logic was flawed. Eustal got 10, the patrons got 3 and the servant got 2. (10+3+2=15) All the PCs have to do is pull the leaver. If they put any other amount in the bucket will tip over and dump it out when the leaver is pulled.

Level 5: The Problem of 5 digits.

Once they pass Odnal’s door they can wander around some more dungeon, but eventually the get to 4th and final puzzle. They reach another room, and once they enter it seals them. Directly after the room seal a panel moves to reveal 5 symbols carved into stone blocks with an abacus style bar extending to the right of each symbol. Each bar has nine beads on it; all the beads are on the right side of the bar. If the beads are moved over to the left side, there is clicking noise. As soon as on bead is moved a leaver will extend from the wall. (The beads are magnetic) An inscriptions on the floor read “Each symbol was a digit in the first language and as value of 1 through 9. Demonstrate the value of each symbol and enter”.

?=@

?=#

?=$

?=*

?=°

Along the walls of the room are written the following equations.

A+B=@$

A+D+C+F=##

C+D+E=#$

C+G=$$

C+D+E+F=$$

E+E=$$

F+D=**

A+D=*@

A+A+A=##

A+A+E=$$

B=*#

A+E=##

A+B+F=°$

G=°°

D+E=@°

Solution:

When I presented this problem to the players, I was surprised that they solved for the equations. The easiest way to do this problems is set up elimination matrix with the 5 unknowns versus the numbers 1-9.

5=@ 6=# 8=$ 3=* 7=°

Gamemaster Notes:

I ran this dungeon and it was very well received. But I did have different types of encounter between the puzzles, and 4 out of 6 party members worked together on the puzzles. Two just kind of sat out of the puzzle process. Only one the non helpers did say "What if one the values is 40". The challenge is to get the PCs to interact with the puzzle as part of the game world and not just as disembodied problem. The specific challenge to these puzzles is the amount of information. Once the PCs sort through the information to determine what is relevant and what isn't then the problems can be easily solved.