PROBLEM MA241 CRUX MATHEMATICORUM V49 No 9

 Pag. 462 - En

Pag. 464 - Fr

ANSWER CiP

$$n=33$$

     Solution CiP

          The same hexagon can be inscribed in the following equilateral triangle with side length 33.

     There is no other option. Indeed, a certain segment of the hexagon, let's say the one of length 4, can only be placed in two places: on the basis of the equilateral triangle or inside an angle.

 

The base and the angle can be any of the three, but due to the symmetries of the equilateral triangle, only one or the other of the two inscriptions is obtained.

$\blacksquare$