(Bloomberg Opinion) -- September is on the horizon, but we’re still rocking out to summer hits. Here at the Conundrums Cabana, that means looking for ways to remix our favorite puzzles of the season.
This week, we’ll mashup our integer sequence and playlist puzzles. I’ve pulled together nine well-known sequences for you to identify. But there’s a twist: As in the playlist puzzle, I’ve left something out of each.
Your first challenge is to name all the sequences. But once you’ve done that, you'll have to keep going. Believe it or not, there’s actually a word hiding in all those digits – and that’s the answer you’re looking for.
1, 2, 2, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, ... 11, 17, 29, 41, 47, 59, 67, ... 2, 3, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, ... 3, 5, 11, 23, 29, 41, 53, 83, 89, ... 7, 31, 127, 8191, 131071, 524287, 2147483647, ... 3, 17, 257, 65537, 4294967297, 18446744073709551617, ... 1, 3, 4, 6, 8, 11, 13, 16, 18, ... 1, 3, 4, 7, 11, 18, 29, 47, 76, ... 1, 1, 2, 42, 429, 7436, 218348, 10850216, 911835460, …
If some of the sequences look unfamiliar to you, feel free to phone your local number theorist or try to look them up on the Internet. As always, when solving Conundrums, you’re free to use any tools at your disposal.
And one note about the names: People often refer to sequences in slightly different ways. For example, 1, 1, 2, 3, 5, 8, 13, … might be called “Fibonacci numbers” or “the Fibonacci sequence.” For our purposes here, don’t worry about articles or words that just indicate that it’s a set of numbers. So 1, 1, 2, 3, 5, 8, 13, … would just be “FIBONACCI.”(1)
If you manage to sort out the answer from among the infinite possibilities -- or if you even make partial progress -- please let me know at skpuzzles@bloomberg.net before midnight New York time on Wednesday, September 2. (Conundrums is off next week, so you get two weeks to solve! If you get stuck, there’ll be hints announced in Bloomberg Opinion Today. Sign up here.) To be counted in the solver list, please include your full name with your answer.
Last Week’s Conundrum
The stars of “Real Genius” accidentally shot a laser through their course registration notes, which were already written in some sort of code.
The solution unfolded from a trick: In each cluster of five-word bits, there was a single set of letters that made each element a word. For the clusters on the left, we needed to add on a “head” at the start; on the right, we needed to add a “tail” at the end.
Putting together those heads and tails and then reading straight down yielded the course name “HONORS BAGGED POPCORN PHYSICS,” which was the answer.(2)