Challenge question #49 (24/04/2017)
Junior Question
After the conclusion of the ping-pong tournament, five participants reported the results as follows:
Alex:
“Don came second. I finished in third place.”
Ben:
“I am the winner. Christopher came second.”
Christopher:
“I came third. Ben came last.”
Don:
“I finished as second. Edward came fourth.”
Edward:
“I was only fourth. Alex is the winner.”
It turns out that each report contained one true and one false statement. Find the order of merit of the competitors.
Senior Question
Suppose a regular square-based pyramid has the following properties:
- Each face has the same surface area.
- The surface area (in m$^{2}$) of the pyramid is equal to its volume (in m$^{3}$).
Find the length of the sides of the pyramid’s base.
