Theorems, like the one currently on the homepage, are puzzles with solutions that come in the form of a word or phrase. Seals, only available to Members, are mini puzzles that can be found throughout this website. In my world, everything, I guess, is a puzzle.

Once you get the hang of a few basic techniques, all the puzzles should start to come together and make more sense—but I'm not so into myself that I can't throw you a few bones. The core thing to remember is that all of my puzzles contain some hint or clue with what you're supposed to do. This includes subtle references in the note I write to the left of the puzzle, the title, and visual clues in the puzzle itself. Think of yourself like a spy, and always pay attention to small details.

If ever you get frustrated with a certain puzzle, remember that my goal isn't to stump you. If I wanted to do that, let's leave no doubt—I'd be able to. Instead, I'm looking for people who want to go on the journey with me, so there will always be clues leading you to a logical process that you can follow to find your way in. At the end of the day, this is supposed to be fun, so I've provided three hints for every Theorem. If you're absolutely stumped, click on the hint buttons on the upper right corner of the page. Using hints may cost you points, but sometimes the satisfaction of a good solve is more important than the resources you used to get there.

Spy or not, you're no James Bond yet, so I've made you a crib sheet. When you're at a loss for how to solve a certain Theorem, try out these techniques:
1. The Internet
Look, I know you don't know everything. I often try to hide clues or pieces of information by hiding them within other information. If you see a quotation about something, a pronoun or obscure reference you don't get, or anything else that you'd like to know more about, it's okay to Google it. Not everyone can know everything about everything (although I like people who do), so you'd just as soon pick up some knowledge while you're at it.
2. Indexing
That means picking individual letters out of some word or group of words, like taking the first letter of every word to spell out a different phrase. It can also mean taking the last letter of every word, the second, third, or fourth letter of every word, or whatever the puzzle implies.

Using an index of 2 on each word below spells, "INDEX":
Hidden inside ideas, between examples.
3. Number And Letter Mappings
When in doubt, see what happens if you translate letters in the alphabet to numbers and vice versa (A=1, B=2, Z=26, etc.). Also, note that you can perform any mathematical operation on letters that you can on numbers. For instance, A + 2 = C.

Mapping the numbers below directly to letters spells, "MAPPING":
13 1 16 16 9 14 7
4. Number Ranges
If you encounter a complete set of numbers from 1 through whatever, it usually means that you should put them back in order.

Using the numbers from 1 through 8 below, you can put the scrambled letters back in order spelling, "ORDERING":
5. Common Ciphers
From time immemorial, people have come up with creative ways to encrypt information. For the most part, if I am using something different or special, I'll give you clues on how to figure out what I've done. Otherwise, take a look at some of the most common ciphers — methods of encoding — that people have used throughout time. We're generally talking about simple stuff, like shifting each letter in the alphabet over one space. Some of the things you see may include shift or Caesar ciphers, substitution ciphers, Morse code, semaphores, pigpen ciphers, and other common methods of scrambling a message to make it less understandable if someone were to intercept it.

Be on the lookout for visual and textual elements that resemble a code or cipher. If you were looking for a picture that showcased long and short elements that could be translated into dots and dashes, try entering that pattern into a Morse decoder tool (each dots-and-dashes letter is separated by a space). Again, don't be hesitant to use the internet as a resource and for tools to help you decode puzzles.

Using Morse code to decipher the message below spells, "CIPHER":
-.-. .. .--. .... . .-.

I'm M, and I'll be your guide. I founded The Master Theorem years ago as a Members-only society of puzzle-solvers, but anyone with the determination to join us can earn Membership by submitting the solution to this or any week's puzzle, called a Theorem. The solution will be in the form of a word or a phrase. As a Member, you'll have the chance to search for hidden Seals throughout the website and compete with other Members by earning points for all of your efforts.

Visit the About page to learn more about The Master Theorem.

Having trouble solving this week's Theorem? Visit the Help page, which has tips and tutorials for puzzle-solvers.