Zodiac 12

In an alternative version of the Greek world, the civilians there also used a calendar with 12 months like the present day one except that the numericals were written in base-12. Therefore, they invented 2 special symbols, denoted as A A for 10 and B B for 11, respectively.

If January 1 year 0 is the day of their first century, which month will it be after 1 , 3 A 7 , 59 B 12 1,3A7,59B_{12} months have passed? (Use decimal 1-12 for January to December respectively.) ![]


The answer is 12.

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1 solution

In base-12, 1 0 12 10_{12} equals decimal 12. Since the year cycle still has 12 months round, we can divide the number 1,3A7,59B with 10 and get B B as a remainder. Therefore, after January, 1+B = 1 0 12 10_{12} =12 or December as an answer.

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