Its easy-1

Number Theory Level pending

Some friends went on a vacation to a resort. It poured sown heavily for 13 days. But when it rained in the morning , the afternoon was beautiful and when it rained in the afternoon, the day was followed by clear morning. Altogether there were 11 very nice mornings and 12 very nice afternoons. How many days did the vacation last?


The answer is 18.

Akash Gupta by Akash Gupta , 21, India

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2 solutions

Stanley Guo
Jan 28, 2015

First, let S stands for Sunny, R stands for Rainy, A stands for Afternoon, M stands for Morning. Originally there can be four types of days: SM+SA, SM+RA, RM+SA, RM+RA. But according to the rule, RM+RM cannot happen, leaving only three types of days. Suppose there are X SM+SA days, Y SM+RA days, Z RM+SA days. So for sunny morning, there are X+Y=11, for sunny afternoon, there are X+Z=12, for rainy day, there are Y+Z=13. Solve the equations, resulting that X=5, Y=6, Z=7.

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Akash Gupta
Jan 26, 2015

Let's assume the number of days as follows: Rain in the morning and beautiful afternoon=X days Clear morning and rain in the afternoon =Z days Number of days with rain = X+Y=13 Number of days with clear mornings=Y+Z=11 days Number of days with clear afternoons = X+Z=12 days Solving above three equations, we get X=7, Y=6, Z=5 Hence, total number of days on holidays = 18

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