Question 49
Silvia has $2006$ identical tiles in the shape of an equilateral triangle and wants to arrange them all on the table without overlapping them and so that each has exactly two sides in common with two other tiles. Can he succeed in his aim? Could he have done it last year, when he had $2005$ cards?
(A) It's impossible either way.
(B) It is possible with $2005$ to weave, but not with $2006$.
(C) It is possible with $2006$ to weave, but not with $2005$.
(D) In these two cases it is possible, but among the numbers greater than $12$ there is at least one for which it is not possible.
(E) It is possible for all card numbers greater than $12$.
(A) It's impossible either way.
(B) It is possible with $2005$ to weave, but not with $2006$.
(C) It is possible with $2006$ to weave, but not with $2005$.
(D) In these two cases it is possible, but among the numbers greater than $12$ there is at least one for which it is not possible.
(E) It is possible for all card numbers greater than $12$.