Pingala the Pirate was well known for many things, most notably the urban legend that he had hidden an enormous haul of riches, but also his poor memory, and his clumsiness. He lost a toe on each foot in a bizarre seahorse attack, then lost both his thumbs after trapping them in a door while escaping from a cyclone. It's amazing he lasted long enough to bury his treasure!

Nevertheless, when he died, his body was discovered with a shovel and a note that had the following sequence written on it: 1,1,2,3,11,20,31,111,202,313,1121,2100,3221

Nobody could work out the meaning of the sequence, but after some exhaustive searching, they found the treasure buried 200 paces to the south west of his body

What was the meaning of Pingala's sequence?


1 Answer 1


Poor Pingala's misfortunes

meant that he couldn't remember arithmetic and had to count on his digits. Alas! He only had four of each and so could count beyond 256. As noted by daw he was trying to keep track of the Fibonacci sequence in base 4.


He started heading North, and wanted to change direction with each Fibonacci number. His experiences with the cyclone meant that he always turned left (or possibly he started heading East and always turned right).

So that

He walked 1 pace North, 1 pace West, 2 paces South, 3 paces East and so on. After walking 233 paces South as his last stretch, he had walked net 169 paces South and 104 paces West (or possibly 169 West and 104 South).

... which is

By Pythagoras a distance of 198.436... paces which is close to 200 paces on a bearing of roughly 211.6... degrees (or possibly a bearing of 238.4... degrees). There may be a little residual error due to the aforementioned cyclone experiences.


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