Question

Give three dichotomous questions that will correctly identify an object’s cardinal or inter--cardinal orientation when answered.

Answer 1

Answer:

For an object there are 8 possible directions . That's 3 bits worth of direction.Now the 3 dichotomous questions which correctly identify an object's cardinal or inter-cardinal orientation are as follow.

Any three questions each of which cuts the number of possible directions in half will do:

1. Does it have a component in a south direction, or is it due west?
2. Is it one of {N,NW,S,SE}?
3. Is it an inter-cardinal direction?

Explanation:

By mapping {No,Yes} to {0,1}, and concatenating the binary answers from left to right to create a number, and using that as an index into the list {E,NE,N,NW,W,SW,S,SE}, you can output the answer.