Why do they like to stay at floor with prime number?

Number Theory Level pending

Four friends, Adit, Budi, Coki, and Dani, are staying at the same hotel. The hotel has 100 floors where the floors are numbered from 1 to 100 in sequence from bottom to top. Each floor has two ladder, namely the upper ladder that serves to connect the floor with floor above and below ladder that serves to connect the floor to the floor below.

Here is some informations about the location of their rooms.

  • They are staying on a different floor where all of their floor numbers are prime numbers.

  • Adit doesn’t dare to stay on the floor with the number is more than 15.

  • If Budi wants to visit his friends' room, then he has to climb the ladder as odd number.

  • Floor number where Coki stay consists of two digits. If the two digits are exchanged its place, then the result is also prime and less than Coki’s floor number.

  • Floor number where Dani stay consists of two digits which its tens digit is 2.

Based on the informations above, the number of possible location of their stay at the hotel is _______ . \text{\_\_\_\_\_\_\_} .


The answer is 40.

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