Number puzzle glossary
Twenty terms every number-puzzle player should know — from digit sum to semiprime, with concrete examples. Most are general number-theory terms; the last several are NumGrid- and Mastermind-specific.
Number-puzzle vocabulary overlaps with elementary number theory plus the deduction-game family that runs from Bulls and Cows (centuries old) through Mastermind (1970) to today’s daily digital puzzles. Knowing the terms shortens problem-solving — if you recognize a number is palindromic, you instantly know fewer position-pair constraints apply.
1. Digit sum
The sum of all digits in a number. NumGrid shows this as a free hint above the grid.
Example: 12345 has digit sum 15.
2. Parity
Whether a number is odd or even — determined by the last digit.
Example: 12347 is odd (last digit 7); 12348 is even.
3. Palindromic number
A number that reads the same forwards and backwards.
Example: 12321, 45654, 11111.
4. Semiprime
A number that is the product of exactly two prime numbers.
Example: 15 (3 × 5), 21 (3 × 7), 35 (5 × 7).
5. Divisor sum
The sum of all positive divisors of a number, including 1 and itself.
Example: Divisors of 12 are 1, 2, 3, 4, 6, 12 — sum 28.
6. Repunit
A number where every digit is 1.
Example: 1, 11, 111, 1111.
7. Pandigital
A number that uses every digit 0-9 at least once.
Example: 1023456789 (smallest 10-digit pandigital).
8. Mastermind
Classic 1970s board game: deduce a 4-peg color code in ≤10 guesses with feedback per peg.
Example: NumGrid is the digit-only version with extra free hints.
9. Bulls and Cows
Centuries-old pen-and-paper game; precursor to Mastermind.
Example: Players guess a 4-digit secret; feedback is "bulls" (right digit, right position) and "cows" (right digit, wrong position).
10. KenKen
A grid puzzle where cells contain arithmetic operations to satisfy.
Example: Created by Tetsuya Miyamoto (2004); 6×6 KenKen has ~10^18 valid configurations.
11. Sudoku
A 9×9 grid puzzle: every row, column, and 3×3 box contains 1-9 exactly once.
Example: Invented in 1979 by Howard Garns; became globally popular after 2004.
12. Nonogram
A logic puzzle (also called Picross or griddler) where numerical clues paint cells to form an image.
Example: A 10×10 nonogram with numbers 3,2,1 in a row means: three painted cells, gap, two painted, gap, one painted.
13. Magic square
A grid where all rows, columns, and diagonals sum to the same number.
Example: The 3×3 Lo Shu Square dates to ancient China; the magic constant is 15.
14. Cryptarithm
A puzzle where letters stand for digits in an arithmetic problem.
Example: SEND + MORE = MONEY has a unique solution: S=9, E=5, N=6, D=7, M=1, O=0, R=8, Y=2.
15. Greens
In NumGrid (and Wordle), feedback indicating the correct digit in the correct position.
Example: Color: vivid green.
16. Yellows
Feedback indicating the digit IS in the answer but in a different position.
Example: Color: gold/amber.
17. Grays
Feedback indicating the digit is not in the answer at all.
Example: Color: muted gray.
18. Information density
A measure of how much you learn per guess. Higher is better.
Example: Opening with 5 distinct digits maximizes information density.
19. Search space
The set of all candidates that still satisfy the known constraints.
Example: NumGrid begins at 100,000; the digit-sum hint cuts to ~3,000; a good first guess to ~50.
20. Deduction game
A game where the player infers a hidden state from feedback over multiple turns.
Example: Mastermind, Bulls and Cows, NumGrid, Cluedo.
How NumGrid uses these terms
Every NumGrid daily puzzle shows two free hints derived from elementary number theory: digit sum and parity. Those two facts alone cut the 100,000-candidate search space to a few thousand before you make your first guess — turning the game from pure guessing into a constraint-satisfaction puzzle in the spirit of Mastermind.
See also: NumGrid vs Mastermind · NumGrid vs Bulls and Cows · Digit sum strategy