# Puzzle-60 | Colliding Stars

Gyani baba is fond of giving new theories about stars. He discovered that there are two type of stars in this universe; one “X” type and another “Y” type stars. In one of his theories about these stars, he states that if n “X” type of stars collide with m “Y” type of stars, the collision results to formation of (m+n ) new “Y” type of stars, elimination of previous n “X” type of stars, and change of type from “Y” to “X” of previous “Y” type of stars. He termed this whole phenomenon as a “Big Bang”. The phenomenon is governed by following rules:

• All the stars collide together at once.
• Further “Big Bang” may occur only after one “Big Bang” has happened. No two ‘Big Bang’s can happen at the same instant .
• The next “Big Bang” can only occur if all the products from previous “Big Bang” collides together.
• In the year 1800A.D., people on the earth were able to count the total no. of stars in the universe. The total count of stars was 144 in the whole universe.

Find the total no. of “Big Bangs” happened till then, if initially there were only 2 stars ?

Solution: 9 “Big Bangs”. If initially, there were two stars , then for the number of stars to increase there must have been one “X” type and “Y” type star each. As you can observe from the problem, “Big Bangs” increases the no. of stars as the Fibonacci series- 1, 1, 2, 3, 5, 8, 13, 21….and so on.
Now, if the total count of stars were 144, then it must be a Fibonacci number, as a sum of previous two Fibonacci numbers which are 55 and 89. Since, 55 is the 10th Fibonacci number, therefore the answer will be 10-1 =9, as already 1 “X” type and 1 “Y” type stars were present.