Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers- [*Trois hexagones et les vingt-huit premiers nombres entiers strictement positifs -neuf d'entre-eux étant des nombres premiers-*].

A structure (white dotted lines) is built using three contiguous hexagons. This structure has V=3*6-((3*1)+(1*2))=13 different vertices and S=(3*6)-(3*1)=15 different sides. The N=V+S=13+15=28 first strictly positive integer numbers {1,2,3,...,28} are located on this structure with the following constraints:

- The P=9 first prime numbers {2,3,5,7,11,13,17,19,23}, recalling that 1 is not a prime number, are on "special" vertices (white figures), when the N-P=28-9=19 remaining integer numbers are on the remaining vertices as well as on the middle of each side (grey figures). Then each of the N integer numbers is used once and only once.
- All the sums of the three different numbers contained on each side (two on the vertices and one on the middle) must be equal to a certain value (
*a priori*unknown):1 + 15 + 28 = 44 1 + 16 + 27 = 44 1 + 21 + 22 = 44 2 + 14 + 28 = 44 2 + 17 + 25 = 44 3 + 18 + 23 = 44 3 + 20 + 21 = 44 4 + 19 + 21 = 44 5 + 12 + 27 = 44 5 + 13 + 26 = 44 6 + 11 + 27 = 44 7 + 9 + 28 = 44 7 + 13 + 24 = 44 8 + 17 + 19 = 44 10 + 11 + 23 = 44

[See the C program used to solve the problem]

(CMAP28 WWW site: this page was created on 02/28/2013 and last updated on 02/26/2018 12:17:43 -CET-)

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