Last Problem:
James visited an island. There were 2 tribes living on this island. The east tribal people always tell a lie. The west tribal people always tell the truth. James saw a guy passing him. He asked the tour guide to ask that guy where he lives. The tour guide asked the guy and came back with the answer: he lives over west. Did the tour guide tell the truth or tell a lie?
Answer:
If the guy was from the west, he should answer the truth: I am from the west. If the guy was from the east, he also should tell a lie: I am from the west. The answer will always be: ‘I am from the west’. So we know the tour guide was telling the truth.
Today’s Problem:
A six digit number 312132 has two one, two twos 2 and two threes . This number has a very interesting attribute: 1 digit exists between two ones, 2 digits exist between two twos and 3 digits exist between two threes. Can we add two more 4s to become an eight digit number and still holding the above attributes plus 4 digits exist between two 4s?