A group of friends and I went on a holiday trip to a hill station.
It rained for 13 days.
But when it rained in the morning, the afternoon was lovely.
And when it rained in the afternoon, the day was preceded by a clear morning.
Altogether there were 11 very nice mornings and 12 very nice afternoons.

How many days did our holiday last?

Solution to the Problem:

The holiday lasted 18 days.

Here is one possibility for the trip:

  DAY     AM     PM  
  1     C     C  
  2     C     R  
  3     R     C  
  4     R     C  
  5     C     C  
  6     C   R  
  7     C     R  
  8     R     C  
  9     R     C  
  10     C     C  
  11     C     R  
  12     C     R  
  13     R     C  
  14     R     C  
  15     C     C  
  16     R     C  
  17     C     C  
  18     C     R  


Mikaylie Roberts sent in the following explanation:
First we need to assign a variable to each of the following sentences.   Rain in the morning with a clear afternoon will be X.   Clear morning and rainy afternoon will be Y.   No rain the entire day will be Z.   The equation for the number of days with rain is shown as X + Y = 13 days.   We get this equation from the amount of days rained is 13 and we know it cannot rain in the afternoon and mornings so we can see that adding the days with morning rain to the days with afternoon rain will give us 13.   The equation for the amount of days with clear mornings is Y + Z = 11 day.   Since we know that there were 11 days with clear mornings we can add the Z to Y.   The equation for the number of days with clear afternoons is X + Z = 12 days.   Using these equations we can find each of the variables.   The variables equal as shown: X=7, Y=6, Z=5.   We can add all of these together to get the amount of days spent on vacation which is 18 days.

Correctly solved by:

1. Brijesh Dave Mumbai City, Maharashtra, India
2. Colin (Yowie) Bowey Beechworth, Victoria, Australia
3. Veena Mg Bangalore, Karnataka, India
4. Kadin Holloway Mountain View High School,
Mountain View, Wyoming
5. Kat Stuart Mountain View High School,
Mountain View, Wyoming
6. Shaelin Wiggill Mountain View High School,
Mountain View, Wyoming
7. Ivy Joseph Pune, Maharashtra, India
8. Hunter Meeks Mountain View High School,
Mountain View, Wyoming
9. Kassadee Lym Mountain View High School,
Mountain View, Wyoming
10. Mikaylie Roberts Mountain View High School,
Mountain View, Wyoming
11. Teancum Piekkola Mountain View High School,
Mountain View, Wyoming
12. Mikenzie A. Roberts Mountain View High School,
Mountain View, Wyoming
13. Adan Vargas Mountain View High School,
Mountain View, Wyoming
14. Ashton Schofield Mountain View High School,
Mountain View, Wyoming
15. Bryson Walker Mountain View High School,
Mountain View, Wyoming