Mark of Zorro
just 3 straight lines through the zed above (fig.
1) form the LARGEST possible number of triangles (see example).
You must also prove that your solution is the best. Hasta
Just for an anecdote, few people know
Williams, the best Zorro ever, was fond of mathematics,
chess and astronomy...
basic geometry knowledge. Category:
dividing-the-plane puzzle. Keywords:
triangles, line segments. Related
- Red monad,
- Stairs to square.
il segno di Zorro
Disegna 3 linee rette sulla zeta qui sopra in modo
da formare il maggior numero di triangoli possibile
Devi anche provare che la tua soluzione è la
migliore possibile... Hasta luego!
Trace trois droites sur le Z de façon à former
le plus grand nombre de triangles possible (selon
Tu dois également prouver que ta solution
est bien la meilleure... Hasta luego!
you can observe in the fig. 3 above, for obtaining
the greatest number of regions when dividing a surface
with straight lines each line segment MUST intersect
ALL the other ones, and by any intersection
point should pass ONLY two lines. The example
in fig. 3C meets all the criteria we have outlined,
thus it contains the greatest number possible of
regions: 7 regions instead of 6.
to our problem the empirical criteria above, we obtain
the following diagram:
the maximum number of triangles obtainable by intersecting
the large Z with 3 segment lines is SEVEN.
Notice that each of the 3 segment lines touches the
two others + the diagonal and both parallel lines forming
the capital letter Z.
Winners of the Puzzle of the Month are: Serhat Duran, Turkey - J.
R. Odbert, USA - Vishal
Dixit, India - Congratulations!
fact behind the puzzle
the number of line segments n,
it can be demonstrated that the maximum number of
portions a convex polygon can be divided with them
is: (n2 + n + 2)/2 [see
fig. 3 above]
but in the case of a concave polygon such as a crescent-like
figure (see fig. 5) it will be: (n2 +
3n + 2)/2
The numbers generated by the first formula (e.g. 2, 4,
7, 11, 16, 22, ...) are called “Pizza