Camelot

Camelot

Treasure

Holy Grail

Monsters

Hedgehog Warrior

Flail Guard
Pikeman

Native Orb

Orb of Trickery

Camelot is a puzzle land that appears inside the Crossroads and Crossroads IV after the player has collected 5 Emeralds. Camelot is the only land that is finite, although it contains billions of cells. The castle is surrounded by a moat of water with several entrances. The main feature is a Round Table, a wall that forms a large circle that the player (but not monsters) can jump over. Knights surround the table, who talk to the player and kill monsters but do not follow the player.

In the center of the table is a Holy Grail, which is worth 10 $$$ and gives the player several charges of Orb of Speed and Orb of Teleport when collected. It also increases the size of future Camelots.

The first Camelot's Round Table has a radius of 28. Each Holy Grail collected increases this by 2 for future Camelots. The moat has a radius 10 larger than its corresponding Round Table. The challenge is to find the center tile, as there are no markings once the Round Table is out of sight.

In Pure Tactics mode, the tables are nested horocycles with increasingly wider gaps between them, and Dead Orbs and Orbs of Safety spawn in the space between a moat and the next Table. The Holy Grails are automatically given to the player at each nested castle.

There is an achievement for getting any kind of shark into the moat of Camelot.

Items

Each Camelot contains only one treasure, the Holy Grail, at its center. Collecting at least one unlocks Orb of Trickery in the Camelot and the Crossroads. Collecting 3 Grails unlocks Orb of Trickery in all lands.

Monsters

The monsters inside the table are the same as in the Emerald Mine, except that there are no Miners. Hedgehog Warriors, Flail Guards, and Pikemen will spawn inside the table.

Perpendicular Bisector strategy

This popular approach^[1] requires no magic, only a large number of Dead Orbs. First, pick a point on the circle and attempt to erect a perpendicular. The angle will not be exact, so this will create a chord.

Second, find the midpoint of your chord (by counting) and attempt to erect a new perpendicular at that point. If done correctly, this will create a new, longer chord. Erase the old chord and repeat until you find the Grail.

It helps to be familiar with several types of straight lines, in order to always be able to pick an option that appears to be close to perpendicular.

The edge of the Round Table in Camelot

Starting with the chord AB, we would like to draw a diameter in order to find the center. If we could draw a perpendicular bisector, we'd have a diameter. But any other chord passing through our chord's midpoint will be longer, and we can iterate until we see the grail. (In Euclidean geometry, this is guaranteed by the Intersecting Chords Theorem: the shortest chord passing through M is the chord which has M as its midpoint.)

The player stands at the midpoint of a short chord

Contraband Compass strategy

Another approach is to bring a Compass into the Round Table. This requires a variety of magical orbs, most crucially the Orb of Space.

In the Caribbean, kill a Pirate 6-7 tiles into an island so they drop a Compass. Use the Orb of Space to move the Compass onto a boat.

Obtain an Orb of Water. If you haven't unlocked it, you can find one dropped by a Water Elemental in the Living Fjord. The Orb of Stunning can help buy time to dock your boat safely before fighting the Water Elemental.

Using your now-magical boat, sail into Camelot, then walk across the Round Table. Use the Orb of Space to bring the Compass to you until you reach the grail in the center.

Relation to hyperbolic geometry

Although the diameter of the first Camelot is fairly small, 55 tiles, there are over 31 million tiles inside the Table. This number grows exponentially as the table size increases. Naively attempting to guess where the Grail is located will likely not get closer than 12-14 tiles away.

Miscellaneous

Attempting to move into the Knights will cause them to cycle through the following messages:

• "I would like to congratulate you again!" Only if the Grail for that table has been found.
• "Find the Holy Grail to become one of us!" Only if the Grail for that table has NOT been found.
• "The Holy Grail is in the center of the Round Table." Ditto
• "I enjoy watching the hyperbug battles."
• "Have you visited a temple in R'Lyeh?"
• "Nice castle, eh?"
• "The Red Rock Valley is dangerous, but beautiful." Only if the player has fewer than 10 Spice.
• "Train in the Desert first!"
• "Our Table seats ____ Knights!" The number grows at each new castle.
• "There are ____ floor tiles inside our Table!" Ditto
• "Have you tried to take a boat and go into the Ocean? Try it!" Only if the player has no Pirate Treasure and no Pearls.
• "When I visited the Palace, a mouse wanted me to go somewhere." Only if the player has not saved a Princess.
• "I wonder what was there..." Ditto
• "Be careful in the Rose Garden! It is beautiful, but very dangerous!"
• "There is no royal road to geometry." (Euclid)
• "There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world." (Nikolai Lobachevsky)
• "It is not possession but the act of getting there, which grants the greatest enjoyment." (Carl Friedrich Gauss)
• "We live in a beautiful and orderly world, and not in a chaos without norms." (M.C. Escher)
• "Thank you very much for talking, and have a great rest of your day!"

References

1. ↑ Comments by Tricosahedron and Fulgur14 on Quest for the Holy Grail