Tuesday, May 26, 2026

SIN Bin: 2018, Problem 2

By Department Faculty

Problem

A line drawing of an equilateral triangle with short hatch marks along the outside of all three edges, indicating that they are reflective surfaces or mirrors facing inward. One corner shows the angle described in the problem.

The true leaders of the world, the Freemasons, grow weary of the constant bickering at the United Nations. As a team building exercise, they kidnap each world “leader” at the UN General Assembly, and place them in a giant escape room together. The room is completely dark, with mirrored walls that form an equilateral triangle. Fumbling in the dark, each leader discovers a flashlight in his or her pocket, capable of producing a beam with an angle of 5 degrees. Assume that the light does not lose intensity when reflected from the mirrored walls, and that the “leaders” are transparent. What is the minimum number of flashlights that must be turned on so that the entire room is lit up?  

  1. 1 
  2. 3 
  3. 12  
  4. 36 
  5. Lighting the entire room is impossible 

Solution SIN Bin: 2018, Problem 2

When you consider all the reflections, one light would do. 

The answer is A.