Competition problem — Number theory

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Number theory Difficulty 3.9 AMC 10/12 Find the answer South Africa

If today is Thursday, what day of the week will it be in 150 days from now?

Pick one

Solution

Every multiple of $7$ represents a full week. Since today is Thursday, in one day's time it will be Friday. Thus each full week after today starts on a Friday and ends on a Thursday. $150$ days divided by $7$ equals $21$ full weeks with a remainder of $3$ days. The $147$ th day from now will thus be a Thursday (end of $21$ st full week), and consequently the $150$ th day from now will be a Sunday.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.