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Mathdle

Glossary

Every term Mathdle uses, in alphabetical order. If something in how to play or tips felt under-defined, it's explained here.

C

Canonical form

The normalised version of an expression that the engine uses to decide whether two submissions are the same. Order inside a + or × chain is sorted, parenthesisation inside a single operator chain is flattened, and identities are stripped. 3 + 5 + 2, 2 + 3 + 5, and (3 + 2) + 5 all reduce to one canonical form. See the math behind Mathdle for the full normalisation rules.

Center tile

The yellow tile in the middle of the board. Every expression you submit must use it exactly once. It's the same constraint the NYT Spelling Bee places on its center letter.

D

Difficulty

Each day ships in four versions: Easy, Medium, Hard, and Impossible. Easy and Medium use only + − × ÷. Hard uses the same four operators but on a stiffer board. Impossible adds mod, √, ^, and !. Progress (points, tier, streak) is tracked separately per difficulty.

Distributing / distribution

Rewriting a product over a sum, or vice versa: 2 × (3 + 4) and 2 × 3 + 2 × 4 are different expressions in Mathdle, even though they evaluate to the same number. This is the single most important mechanic for stacking points; see the tips page for how to milk it.

E

Euler (tier)

The top of the eight tiers. Awarded only when you find every catalogued expression for the puzzle — 100% of maxPoints. On Easy and Medium it's reachable in a sitting; on Impossible it's rare and usually takes most of a day.

Exact rational

Mathdle evaluates expressions over exact fractions (BigInt numerator and denominator), not floats. That's why ÷ is accepted when the result is a whole number but rejected when it would round: 56 ÷ 8 = 7 works; 56 ÷ 6 does not, because the engine refuses to silently truncate.

Expression

A single submission: a sequence of tiles, operators, and parentheses that evaluates to the day's target. 3 + 9, (7 − 2) × 4, and 5! ÷ 2 + 1 are each one expression. Expressions are the unit you score.

F

Factorial (!)

Impossible mode only. n! is the product of every positive integer up to n: 5! = 120, 6! = 720, 7! = 5040. The operand must be a non-negative integer in the range 0–8. 0!, 1!, and 2! are rejected as identities (they reduce to 1, 1, and 2 with no real work done).

G

Genius (tier)

The seventh of eight tiers, awarded at 85%of the puzzle's maxPoints. Genius is the “you really solved this” mark; Euler is the “you found literally everything” mark above it.

I

Identity

An operation that doesn't change its operand. Mathdle rejects identities so you can't pad expressions with no-op tiles. The full list: x + 0, x × 1, and on Impossible x^1, x^0, 1^x, x mod 1, √1, and 0!/1!/2!. Any subtree matching one of these patterns disqualifies the whole expression.

M

Mod (modulo)

Impossible mode only. x mod y is the remainder of integer division: 17 mod 5 = 2, 20 mod 4 = 0. Both operands must be integers and y ≠ 0; x mod 1 is rejected as an identity. Keyboard shortcut: %.

O

Operator chain

A run of the same associative operator without intervening parentheses. 2 + 3 + 5 is one + chain; 2 × 3 × 5 is one × chain. Canonical form sorts operands within a chain and ignores internal parenthesisation, so (2 + 3) + 5 and 5 + 2 + 3 are the same expression.

P

Pangram

An expression that uses all seven tiles exactly once. Most puzzles have at least one pangram; many have several. Worth a fat point bump — see the bonus below.

Pangram bonus (+7)

A flat +7added on top of the normal tile points for any expression that's a pangram. A 7-tile expression normally scores 7 (1 per tile); as a pangram it scores 14.

R

Real-rational engine

The internal evaluator. Every intermediate value is stored as an exact fraction over BigInt, so ÷behaves like real division (not integer division) and rounding never sneaks in. If a calculation can't be represented exactly as a rational — for example √7— it's rejected. See the math page for the gory details.

S

Square root (√)

Impossible mode only. Accepts perfect squares and nothing else: √4 = 2, √49 = 7, √144 = 12. √7 is rejected because it isn't an integer; √1 is rejected as an identity. The square-root tile lives on the operator row; there is no keyboard shortcut.

Streak

The number of consecutive days you've completed at least one puzzle (any difficulty). Computed in UTC. A streak is alive as long as your most recent counted activity is today or yesterday.

Streak freeze

A one-day buffer that protects your streak if you miss a single day. You start with one freeze. When you complete a puzzle after a one-day gap, a freeze is consumed automatically and yesterday is back-filled. A fresh freeze is granted every 7 clean days, capped at 2 banked. Miss two days in a row, or miss a day with no freeze in the bank, and the streak resets to one.

T

Target

The integer your expressions need to equal. Shown above the board. It's the same target for every player on a given day and difficulty.

Tier

Your rank within a single puzzle, based on the fraction of maxPoints you've found. The eight tiers and their thresholds:

Tile

One of the seven numbers on the board. Each tile is a positive integer and has a distinct identity even when two tiles share a value — a board with two 5s gives you two separate tiles, and using both is fine (and required for a pangram). Each tile can be used at most once in a single expression.

Missing a term? It probably belongs in how to play, tips, or the math behind Mathdle.