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

Question

Advanced Placement (AP)

Joanna

18 June, 21:17

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

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Answers (1)

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Steven · Answer 1

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:

Does it have a component in a south direction, or is it due west? Is it one of {N, NW, S, SE}? 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.