How can I turn a B*-tree into a puzzle?

Question

My players, being quite terrified of the consequences of injury (less research time), have asked me for a series of magical puzzles for their next adventure. I have decided that, roughly, it will follow a 5-room adventure format.

The first puzzle entails word puzzles, and the third will entail complicated truth tables. I want the second puzzle, however, to be the exploration from the inside of a b*tree, normally used in database indexes.

Functionally it is a logical tree structure that rebalances on new inserts. While intuiting its rules will make a fine puzzle, I'm missing one piece:

What is an acceptable goal for a puzzle involving a b*tree, and how would you frame this goal?

For example:

[You] 4 magi walk into a giant cave, floored with clouds. (The more fantastic the better). There are golden platforms, flowing in, that seem to be linked with fine silver threads and tiny copper needles attaching them to other platforms. There is a barred gate on the other end of the clouded cave. There is an air of unfulfilled potential here.

... which does nothing to explore the parameters of the puzzle or articulate the central challenge.

Alternatively:

There is a mound of numbered tablets and a giant wormy tube in front of them. As they walk through the tube with a tablet, the tube squirms around to point to a different nodule with stand for a tablet.

Answer 1

You walk into a giant cave, floored with clouds. There is a single golden platform, floating in the sky near the precipice you stand on, like a boat docked on the shore. Engraved on it is the arcane rune XIII. A short distance further you see your destination: another platform extending out into the clouds.

The platform is large enough for all of you and supports your weight. On it you find nearly two dozen glass bottles, each appears to hold in it a cloud, and each bears a different arcane rune, I-XI. XIII is notable absent. Upon unstoppering the last bottle, a cloud in the shape of the rune appears, and a fine silver thread attaches it to the golden platform which begins to shift. Upon opening another, "XIV", it too has a similar effect. You wait for the room to stop shifting.

Unfortunately you're further from your goal, and only the golden platform XIII can support your weight. Placing the stoppers back on the bottles, however, sucks their ethereal clouds back in, leaving the room once again how you found it. You have an idea, though, and upon unstoppering bottles "I" and "II", you've made it slightly closer to the other side.

After just two more opened bottles, the platform on which you stand has gotten close enough to the stone pier for you to safely jump across.

You continue on your epic quest, more glad than ever that you decided not to study computer science...

Answer 2

I provided two puzzles:

You are standing on one side of a bridge which terminates before its middle in a golden cloud. The other side of the bridge is offset, but there are slight streamers of golden trailing from the edge of the railing-less bridge, and the winds howl around you. Inscribed in the base of the cloud is XIII. On the cloud there are twenty-one bottles, each inscribed with I to XI. The bottle marked XIII is open, and its cork is lying to the side. To cross, it seems that you need to uncork the right bottles.

This was a simple experimentation room where brute force would quite quickly find the answer. My players took the bottles off the cloud, and I used cards to represent the various numbers. I entered the numbers into the applet on my computer so I didn't have to balance the tree by hand. Rego Herbam was very useful to the players when they stoppered bottle 13 and needed to unstopper it quickly.

Generally, quite interesting time of experimentation.

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You are standing in a large, marble-floored room. A beam of 6 colours of light is shining through the center, Red, Orange, Yellow, Green, Blue, Violet. There are twenty six bottles on one side of the room, each labeled with a letter of the alphabet. The bottles R, O, Y, G, B, and V have been shattered. There are six lenses, each of one of the colours set into the other side of the room.

A warning hovers over the bottles, "There is not air enough for 6 of us."

As my players understood how the sorting worked (I pulled out my icehouse pieces and combined them with the cards to show how the prisms split the beams) this was solved relatively quickly and successfully.

A novel puzzle that was a moderate success.

Answer 3

Actually if you are referring to a Binary Tree, then you can have some fun with getting your players walk from node to node trying to map down a correct sequence of "Pre-Order", "In-Order", or "Post-Order". http://en.wikipedia.org/wiki/Tree_traversal

Here's a cheat guide for pre-order notation: If all players start in the Root Node (which is drawn at the top of the tree (North) with up to two paths leading down (south)), they write onto a piece of paper the node they are currently in (because they haven't been there before), then with their right hand on the wall of the cave, they choose the left path (rightmost path from their perspective as they look south), they follow the path with their hand until they reach the next node... where if it is a newly unvisited node - they write down the name of this new node onto the piece of paper, they then follow the path their hand leads them (which means that if this is a dead end, they trace their route back out again).

These steps are repeated again and again until they get back to the Root Node they started at (and with all paths from that root node visited). The piece of paper they were writing on is the "pre-order" notation for the entire binary tree.

For post-order all that is needed instead is to write down the name of every node visited on the piece of paper (after the previous written) and erase any previous mention if it was visited before. The paper will now provide a list of the post-order from the sequence of node names that were not erased/crossed out.