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


255. Some simple machines

A. In a single fixed pulley system (below left), the force to load ratio is 1:1.  In other words, the force pulling down on one side equals the force pulling up on the other side.  In a single movable pulley system (below right), the force to load ratio is 1:2, or a given force balances twice the load.
(If you have these two scenarios in more, um, inclusive pictures, please send.)


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)