Professor Erasmus has returned from his saturday walk in the park. He has counted the number of trees in the park and also the number of lines formed by these trees. Professor Erasmus claims that
- there are exactly 26 trees in the park,
- there are exactly 306 (distinct) lines formed by these trees,
- and that none of these lines does contain four or more trees.
(When the professor speaks of trees on a line, then he means that the centerpoints of the trees lie on a common line.)
We wonder: Has the professor once again made one of his well-known mathematical blunders, or does such a collection of 26 trees indeed exist?