MathDB

In a regular polygon with

134

sides,

67

diagonals are drawn so that exactly one diagonal emerges from each vertex. We call the length of a diagonal the number of sides of the polygon included between the vertices of the diagonal and which is less than or equal to

67

. If we order the lengths of the diagonals in ascending order, we obtain a succession of

67

numbers

(d_1,d_2,...,d_{67})

. It will be possible to draw diagonals such that
a)

(d_1,d_2,...,d_{67})=\underbrace{2 ... 2}_{6},\underbrace{3 ... 3}_{61}

?
b)

(d_1,d_2,...,d_{67}) =\underbrace{3 ... 3}_{8},\underbrace{6 ... 6}_{55}.\underbrace{8 ... 8}_{4}

Problem Statement