Methodology

NumGrid publishes one fresh number-guessing puzzle every UTC day. Targets are 4- or 5-digit integers; feedback follows Mastermind conventions; every puzzle is proven solvable within the published guess budget before publication.

Target selection

The daily target integer is selected by a deterministic generator seeded from the calendar date. The candidate pool is all positive integers of the day's digit length (4 digits on easier days, 5 digits on harder days) with three exclusions: palindromes (read the same forward and backward), all-same-digit numbers, and strictly sequential digit runs (12345, 67890). All three classes are mathematically valid but reduce the deductive challenge meaningfully, so we exclude them from the target pool.

Repeated digits within a non-trivial integer are allowed. The puzzle correctly handles repeated digits in both the target and the guesses per standard Mastermind rules: each digit in the guess gets feedback based on its occurrences in the target relative to how many of that digit have already been credited in the guess.

Feedback rules

Each guess returns three categories of per-digit feedback:

• Green — this digit appears in the target at this exact position.
• Yellow — this digit appears in the target but at a different position.
• Gray — this digit does not appear in the target.

Repeated digits in the guess receive feedback per the position-and-count rule. If the target contains one 7 and the guess contains two 7s, the first 7 in the guess (left to right) gets green or yellow as appropriate; the second 7 gets gray. This is the standard Mastermind convention and matches the player intuition that repeated guesses do not gain extra credit.

Solvability validation

Before publication, the in-house solver attempts to solve every candidate puzzle within the published guess budget using optimal-information strategy. The solver picks the guess that maximizes expected information at each step (minimizing the expected size of the remaining candidate set). If the solver cannot reach the target within the guess budget, the puzzle is rejected and regenerated.

The optimal-information strategy is documented in the strategy guides. Real human players use heuristics rather than full expected-information calculation, so the solver's success rate on a puzzle is an upper bound rather than a typical player's experience. The guess budget is calibrated so a competent human player using common heuristics solves the puzzle about 80% of the time on a first try.

Difficulty calibration

Difficulty is not just a function of digit length. Two 5-digit puzzles can have very different difficulty profiles based on the specific digit pattern in the target. A target with three repeated digits (like 73737) carries less per-guess information than a target with five distinct digits (like 13649) because repeated digits collapse the feedback signal.

We use a pilot-tester pool (~20 testers per puzzle) to measure solve counts and times on candidate puzzles. The published puzzle for a given day is one whose pilot metrics fall inside the target difficulty band for that day. Mondays through Wednesdays target an easier band; Thursdays through Sundays target a harder band.

Classroom and teacher use

NumGrid started as a classroom mental-math warm-up. We maintain a teacher-friendly experience by keeping past puzzles permanently accessible, supporting printable PDF export of any past puzzle for offline classroom use, and publishing a teachers' section with suggested classroom uses, grade-appropriate puzzle ranges, and strategy talking points.

Teachers do not need to create an account to use NumGrid in a classroom. All teacher resources are downloadable directly without signup, and the puzzles themselves work in any browser without an account.

Frequently asked questions