Number of Days

Number Theory Level pending

What is the minimum necessary number of years, so the sum of its days is a multiple of 4?


The answer is 3.

Vitor Curtarelli by Vitor Curtarelli , 30, Brazil

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2 solutions

Kay Xspre
Jan 28, 2016

One may think it took 4 years, but every 4th year, there will be a leap day (29th February), adding one more day to the total number of day. To eliminate this reminder, you need to wait 4 cycles, each of which took 4 years, hence it took 16 years

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But 4 ∣ ( 365 + 365 + 366 ) 4 | (365 + 365 + 366) .

Arulx Z - 5 years, 4 months ago

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That's what I thought too.

Abdur Rehman Zahid - 5 years, 4 months ago
Vitor Curtarelli
Jan 29, 2016

Year A has 365 days. So does year B and year C. But, year D has 366 days, which, in sum, results 1461 days, in every 4 years. So, you'd need 4 cicles (of 4 years), to have a number of days multiple of 4. Therefore, the number of years is 16.

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