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, 2019

Number theory Difficulty 1.4 Junior Find the answer Canada

A piano has 52 white keys that occur in a repeating pattern of ABCDEFG. The first white key is A. What letter is associated with the 33 $^{rd}$ white key?

Pick one

Solution

The repeating pattern of ABCDEFG has 7 white keys.

Since the first white key is A, the pattern repeats after each number of keys that is a multiple of 7.

Since 28 is a multiple of 7, then the 28 $^{th}$ white key is G and so the 29 $^{th}$ white key is A, the 30 $^{th}$ white key is B, the 31 $^{st}$ white key is C, the 32 $^{nd}$ white key is D, and the 33 $^{rd}$ white key is E.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.