How do you solve a 'grid logic puzzle' (like 'who owns the fish' style puzzles)?

Create a grid of all possibilities, then eliminate cells using clues — a cell is eliminated if any clue makes it impossible, until each row and column has exactly one solution Start with the most complex clue and work down to simpler ones Guess the answer and verify it against all the clues Ignore the clues and work out all possibilities mathematically

What is 'constraint satisfaction' and why is it important in computer science?

Finding a solution that satisfies all given constraints simultaneously — used in scheduling, circuit design, planning, puzzle-solving, and AI Making computer programs run without errors by satisfying all requirements Managing user restrictions on what they can do with a computer system A legal process for resolving disputes about software licensing

In Sudoku, if the number 7 already appears in the first row, what can you conclude?

7 cannot appear anywhere else in the first row — this eliminates 7 as a possibility for all other empty cells in that row 7 must appear in every other row as well — it balances out 7 cannot appear in any row above the first row Nothing — each cell is independent in Sudoku

What is 'pigeonhole principle' and how can it help in codebreaking?

If you have more items than containers, at least one container must hold more than one item — in codebreaking: if a cipher has fewer keys than messages, some messages share a key Physical pigeons were used to carry encrypted messages before radio was invented If a key can be used more than once, it must be in a 'pigeonhole' style cipher A principle that states all possible solutions must be tried before giving up

What is 'binary' and why do computers use it?

A number system using only 0 and 1 — computers use it because electronic switches have two states: on (1) and off (0), making binary a natural fit for electronic circuits A system that codes information using pairs of letters (bi=two, nary=letters) Binary is used because it's faster than decimal for complex calculations A number system used only in cryptography — normal math uses decimal

What is a 'substitution cipher' at its most basic level?

A cipher where each letter (or symbol) in the plaintext is replaced by a specific, fixed substitute — the same letter always maps to the same symbol A cipher where letters are substituted with their numerical positions (A=1, B=2...) Replacing entire words with other words from a codebook A cipher that uses mathematical substitution to produce a different length output

What makes a simple substitution cipher vulnerable to frequency analysis?

Every plaintext letter maps to the same ciphertext symbol always — so the statistical frequencies of letters in the language are preserved in the ciphertext The cipher uses too small a key — only 26 possible keys make it easy to brute force Substitution ciphers can only encrypt letters, not numbers or symbols The pattern of word lengths is visible in the encrypted text

What is an 'acrostic' and how has it been used as a form of steganography?

A text where the first letters of each line, sentence, or paragraph spell out a hidden message — used throughout history to hide messages in plain sight A type of crossword puzzle where all answers begin with the same letter A poem that describes how to decrypt a cipher An ancient Greek writing system that predated the modern alphabet

What is 'set theory' and how does it apply to code analysis?

The mathematics of collections — sets can be intersected (elements in both), unioned (elements in either), and differenced — useful for comparing which letters appear in different message sections A system for organizing physical objects into boxes and categories Mathematical rules for working with sets of keys in encryption The theory that codes can only be broken with the right set of tools

What is 'cryptarithmetic' (like SEND + MORE = MONEY)?

Mathematical puzzles where letters represent unique digits and the equation must be satisfied — finding which digit each letter represents requires logical elimination and trial-and-error Arithmetic used by cryptographers — a secret form of mathematics taught only to codebreakers The art of encrypting arithmetic equations so they can be solved without knowing the numbers A method of hiding messages inside arithmetic problems