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Gödel, Escher, Bach

A cache by mmammel Send Message to Owner Message this owner
Hidden : 11/20/2007
4 out of 5
3 out of 5

Size: Size:   regular (regular)

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Geocache Description:

Solve the puzzle to find the cache coords in Patapsco Valley State Park.

This puzzle cache is a tribute to the excellent book “Gödel, Escher, Bach: an Eternal Golden Braid” by Douglas Hofstadter (but you do not have to read the book to solve this). The first puzzle will give you a keyword to build a Polybius square (first fill in the keyword, then the rest of the alphabet in order) that will be used by the other two puzzles. The final location will be at N39 AB.CDE W076 FG.HIJ.

1. Gödel Encoding. To prove his Incompleteness Theorem of mathematical systems, Kurt Gödel used a simple encoding which assigns a series of symbols or numbers to a unique number. The five letter keyword for the Polybius square is represented by this Gödel number:


2. Escher Ribbons. Dutch graphic artist M. C. Escher is famous for paintings of impossible constructions, self-reference, and mathematical relationships. The diagram below is similar to Escher’s “woven ribbon” tiling. Use this diagram to spell out the Minutes (AB.CDE) of Latitude using the Polybius square.

3. Bach Crab Canon. German composer J.S. Bach is one of the most famous composers of all time. The music below is based on the “Crab Canon” (a Retrograde Canon) from Musical Offering. Use the music to spell out the Minutes (FG.HIJ) of Longitude using the Polybius square. For fun, you can play this music file to hear the composition being played on the piano. It is not necessary to play it for solving, but possibly it will help you follow the way the music is played.

Hike: Park at the coordinates in the parking waypoint below. Hike North along the yellow blazed trail along the road for 400 yards, then at the gate by the road, cross the road and proceed about 30 paces further North to the trailhead (listing coordinates). Follow this trail (white blazes) to the cache area. Approved by MD DNR.

FTF honors go to Vinny & Sue Team

STF Janji

3TF jeffandchris5678

You can check your answers for this puzzle on

Additional Hints (Decrypt)

[puzzle hint: Escher] pbybe vf abg eryrinag.
[cache hint:] svaq tbyqra oenvq va ubyybj gerr.

Decryption Key


(letter above equals below, and vice versa)

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