## Leonhard Euler

## Problems of January

1) Find the first three nonzero terms in the Taylor series for tanx on [ , ].

Selin Deniz Akdoğan

2) The hacker wants to crack the password to get the elixir of eternal life. The password consists of 10 digits. The digits are chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. This hacker likes the prime numbers and thus, the passwords that he tries has to include all prime numbers from the set. What is the probability that he finds the correct password?

3) A wizard writes MALAMANDER on her separate cards. She now wants an elf to shuffle the cards randomly with the condition that neither two A nor two M are next to each other. Yet putting 3 A next to each other is not a problem. The total number of ways the elf can shuffle the cards will determine his lifetime. How long will the elf live?

Eda Toprak