In a certain tribe, you have a certain amount of tribal offerings, at the start of year 1. However, at the start of each year (including this one), you must feed the black hole with a number of tribal offerings equal to the size of the black hole. On year 1, the black hole starts as size 1 and doubles each year that you pay the tribal offerings. (If it was 4, it's 8 now.) If you can't pay this cost, the island will explode in the middle of this year.

However, your workers are very industrious with investing, and always manage to double the number of tribal offerings that you had at the beginning of the year after paying the black hole.

For example, if you started with 4 offerings: (B = beginning of year before feeding the black hole, A = after you fed the black hole, E = end of year after your tribal offerings have doubled)

--B-A-E
1|4 3 6
2|6 4 8
3|8 4 8
4|8 0 0
5|0

Since there wasn't enough to pay 16 tribal offerings, the island lasted 5 years.

How would you find the number of turns this island would last if you started with x tribal offerings?

(In reply to Problem clarification? by tomarken)

Heh that is was wording from a previous life of the problem. I will see if I can fix it.

The problem defines what "lasts" equals, so although it might have had different definiitons if an explicit example wasn't given, the official definition is it lasted until year 5 if it explodes at the beginning of year 5.

If I was going to write the problem again, I would have said it lasts 4 whole years or something like that so whether or not you consider the first part of 5 years, the answer is the same.

Posted by Gamer on 2006-03-22 16:10:57