Days of Rain

Computer Science Level 2

After $n$ days of school vacations, a student observes that:

I) It rained seven times in the morning or afternoon;

II) When it rains in the morning, no rains in the afternoon;

III) There were five afternoons without rain;

IV) There were six mornings without rain.

What is the value of $n$ ?

1 solution

Marco Luca Sbodio
Jan 21, 2015

Let

Then

from statement I) we can write $M_R + A_R = 7$
from statement III) we can write $A_S = 5$
from statement IV) we can write $M_S = 6$
finally, from problem statement we can write $M_R + M_S = n$ and $A_R + A_S = n$

Therefore we end up with these three equations with three variables:

$M_R + A_R = 7$

$M_R + 6 = n$

$A_R + 5 = n$

by summing the last two equations we get

$M_R + A_R + 11 = 2n$

and by substuting the first equation we get

$18 = 2n$

from which n = 9! Obviously, $M_R = 3$ and $A_R = 4$ ... which complies with statement II)