Simple Puzzle of Three Hexagons by pmoews

Last crawled date: 3 years, 1 month ago

A simple puzzle based on the hexagonal tortoise problem.
The hexagonal tortoise problem was proposed by a Korean mathematician some 300 years ago. The N vertices of a hexagonal array are given numbers from 1 to N. The numbers are arranged so that the sum of the six integers at the vertices of each hexagon is the same. The original "magic" tortoise pattern, which contains 9 hexagons, was published in 1700. The sums of the integers at the vertices of each hexagon are 93. See - https://en.wikipedia.org/wiki/Hexagonal_tortoise_problem
Tortoise.stl is a copy of this pattern; it can be used to check the sums. Note that the central hexagon is consecutively numbered; a clue to its construction ?
A solution to the 8 hexagon problem is apparent in tortoise.stl. Remove vertices number 1,29 and 30. Adjust the integers on the remaining 27 vertices so that they range from 1 to 27. The sums of the integers at hexagon vertices will be 87.
The puzzle, hex_puzzle.stl, is composed of three hexagons with vertices numbered from 1 through 13. Solutions occur where the sums of the integers at the vertices of each of the hexagons range from 34 through 50. A solution for the sum 43 is printed on the puzzle.
Tokens labeled from 1 through 13 are provided. The problem is to place the tokens in the puzzle finding solutions other than 43, particularly 34 and 50.
OpenSCAD code is included.