MathDB

Version for Nordic Countries Six pine trees grow on the shore of a circular lake. It is known that a treasure is submerged at the mid-point

T

between the intersection points of the altitudes of two triangles, the vertices of one being at three of the

6

pines, and the vertices of the second one at the other three pines. At how many points

T

must one dive to find the treasure?
Version for Tropical Countries A captain finds his way to Treasure Island, which is circular in shape. He knows that there is treasure buried at the midpoint of the segment joining the orthocentres of triangles

ABC

and

DEF

, where

A

B

C

D

E

and

F

are six palm trees on the shore of the island, not necessarily in cyclic order. He finds the trees all right, but does not know which tree is denoted by which letter. What is the maximum number of points at which the captain has to dig in order to recover the treasure?
(S Markelov)

Problem Statement