# Lucky Seven

Here are seven tricky puzzletts, all dealing in some way with your friend, the number. Some are simple algebra problems, others involve numbers and logic, and a few wander completely out of the bounds of mathematics altogether into obscure trivia.

Unlike most of our puzzles, we allowed people to submit answers to this puzzle collection. Please note that for any puzzle where we want people to send in their solutions, we will note it in the puzzle.

1. A length of a rope is 30 feet, plus half its total length. How long is the rope?
2. What's the next number in this series: 1,000; 1,000,000,000; 1,000,000,000,000,000,000,000,000,000; 100; 0; 4; 8; 3?
3. "Seven of Nine" is the curvaceous cyborg on Star Trek: Voyager. Who is "One of Six to Eight"?
4. Solve for x in this infinite summation: sqrt(x + sqrt(x + sqrt(x + ... ))) = 2
5. There are _ 1's _ 2's _ 3's _ 4's _ 5's _ 6's _ 7's _ 8's _ 9's and _ 0's in this sentence. Fill in the blanks with the correct digits to make the sentence true.
6. What's next: 1, 2, 5, 14, 42?
7. Quick! What is c in petasmoots per femtotribulation?