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 {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28} 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
```
The colored lines (starting with 1 -red, at the center of the structure- and ending with 28 -yellow, in the middle right-) display the natural order of the integer numbers.

[See the C program used to solve the problem]

(CMAP28 WWW site: this page was created on 02/28/2013 and last updated on 01/23/2023 18:54:27 -CET-)

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