# Vacation duration puzzle

I was faced with the problem, that I don't think has a solution. Whether someone can confirm my guesses or prove otherwise.

Following problem :

Joe and Tony take a vacation at Summer camp. During the vacation, they both either played tennis in the evening or practiced Yoga in the morning, ensuring that they do not undertake both the activities on any single day. There were some days when they did nothing. Out of the days that they stayed at the camp, they involved in one of the two activities on 22 days. However, their counselor while sending an end of vacation report to their parents stated that they did not do anything on 24 mornings and they did nothing on 12 evenings. How long was their vacation?

A) 36 days B) 14 days C) 19 days D) Cannot be determined E) 29 days

• Please provide the source of the problem. Commented Sep 9, 2019 at 11:48
• it seems like that this puzzle comes from elsewhere. please provide the source. unattributed work may get downvoted or even closed. happy puzzling ;) Commented Sep 9, 2019 at 11:52

E. 29 days.

Because:

We should look at the number of session (morning or evening).
We know they played either tennis (T) or yoga (Y) on 22 occasions.
Therefore, Y + T = 22
We know for 24 + 12 sessions they did nothing. let's call it a session skip (sS).
sS = 24 + 12

Let's define the total number of sessions (tS) as:
tS = Y + T + sS
Y + T = 22
sS = 24 + 22
tS = 22 + 24 + 12 = 58.

There are 2 sessions in a days, so their vacations was 29 days long.

My pick is

E. 29 days.

Explanation

Each of the 22 days of activities, left either a morning or evening free accounting for 22 of the mornings and evenings nothing was done. The remaining 14 mornings and evenings with no activities can be accomplished in 7 days. 22 days plus 7 days or doing nothing == 29 days.