In a block of 100 flats a painter is kept employed by painting one flat each month of January to November the flats are painted in the same order and he takes holiday every December if my flat was last painted in August 2010 when will it be next painted
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you can disregard december for this question, as nothing happens then, so you can consider it an 11-month year. you would do \(100 \mod 11 = 1\), so add one month to your previous painting, i.e. the next painting will be in an september, and because 11 goes fully 9 times into 100, you add 9 years, so the next time will be september 2019