Estimable reader: A dialogue appended to problem 42 highlights an unsettling outcome of a widespread approach to mathematics education.


254. Even seven


In the diagram, △ABC is divided into seven triangles of equal area.
Given BC = 12 cm, determine the length of EC.


253. A tournament


The diagram shows an elimination tournament amongst six teams, A-F.  The winner of each game follows a blue line.

After the tournament, each team made a statement, as follows:
A: We lost our first game, but to win the tournament, we would have had to win three games.
B: We did not play A.
C: We lost to D.
D: We played B in our second game.
E: We did not play C.
F: We won our first game.

Determine the team bracket, α to ζ.

(from Twitter)


252. Folded triangle


In the diagram is right isosceles triangle ABC, with ∠A = 90°, AB = AC = 4 cm.  Point B is folded over PQ so that it overlaps point D on side AC, and AD = 3 cm.  Determine the length of PQ.

(from Twitter)