Leading zeroes are allowed when you play a digit deduction game that searches the full three-digit space from 000 to 999, including the original three-digit code in Crack the Code. Every slot in a three-digit code is a separate digit position, and a code like 075 is just as valid as 750 or 507. The solver treats each position independently rather than treating the code as a number, so a 0 in the hundreds slot is a normal candidate. The exhaustive proof built into Crack the Code enumerates all 1,000 zero-padded candidates from 000 through 999 and filters them through the two clues, leaving exactly one valid code. That means any leading-zero candidate that satisfies both clues is automatically a fair answer. This article explains how the search space includes leading zeroes, how the duplicate-safe scoring prevents inflated wrong-place counts, how the unique answer is derived from just two clues, and what input, scoring, and reset rules apply when you play.
How Leading Zeroes Work in the 000 to 999 Search Space
A three-digit code game that respects leading zeroes treats every code as three independent digit positions, not as a decimal integer. The complete search space for Crack the Code is therefore 000, 001, 002, and so on through 999, which is exactly 1,000 candidates. The two clues shown on the puzzle card are 527 with two exact and zero wrong place, and 750 with zero exact and three wrong place. Both clues are evaluated against the full padded range, so a candidate whose hundreds digit is 0 is checked exactly the same way as a candidate whose hundreds digit is 7.
The independent proof shipped with the game pads every integer from 0 through 999 with leading zeroes, runs the scorer on each one, and keeps only the candidates that satisfy both clues at the same time. That traversal returns exactly one code: 507. Because the proof enumerates 000 through 999 rather than 100 through 999, codes like 075 or 050 are real candidates whenever they happen to match the clues. There is no hidden rule that excludes any leading-zero combination, and the page FAQ states this directly: a leading zero is a normal digit position.
Reading the Clues: Exact Versus Wrong Place
Each clue is two separate counts. The exact count counts digits that match the solution digit at the same position. The wrong place count counts digits that exist in the solution but at another position. A single solution position can only contribute to one count, so a digit that is exact in slot one cannot also be counted as wrong place in slot one.
The scorer enforces this in two steps. First it removes every exact pair from the solution and from the guess. Then it compares the frequency counts of the remaining unmatched digits. A digit that appears twice in the guess but only once in the leftover solution contributes to wrong place at most once, even when the guess contains two copies of it. This prevents the classic inflation bug where a guess like 500 against a solution of 507 would otherwise read as 3 wrong place instead of the correct 2 exact and 0 wrong place.
| Guess | Against Solution 507 | Exact | Wrong Place | Why |
|---|---|---|---|---|
| 527 | 5, 2, 7 | 2 | 0 | 5 and 7 are exact; 2 is absent from the solution. |
| 750 | 7, 5, 0 | 0 | 3 | All three digits exist but every one is in a different position. |
| 057 | 0, 5, 7 | 1 | 2 | 7 is exact in the final position; 0 and 5 are present but exchanged. |
| 500 | 5, 0, 0 | 2 | 0 | 5 and the first 0 are exact; the extra 0 has no second 0 to pair with. |
| 123 | 1, 2, 3 | 0 | 0 | None of the digits appear in 507. |
The 500 row is the clearest demonstration that multiset accounting matters. A naive scorer would credit an extra wrong place for the duplicate 0. The actual scorer sees only one unmatched solution position, so the second 0 has nothing to attach to and contributes zero.
How to Solve the Three-Digit Code From Two Clues
- Start with the displaced-only clue. The clue showing 0 exact and 3 wrong place tells you that all three of its digits (7, 5, and 0) are in the solution, just not in the positions you guessed.
- Use the second clue to fix the order. The clue showing 2 exact and 0 wrong place places two of those three digits in their exact slots. Identify which two digits in 527 are exact and place them in slots one and three.
- Drop the third digit into the remaining slot. The digit that is absent from the second clue (2 in this case) cannot be in the solution at all, so the remaining slot is filled by the third digit from the displaced-only clue.
- Type the full code and submit it. Use the 10-digit keypad, the physical 0 through 9 keys, or a touch device. Three filled slots and a complete submit is the only path to scoring.
- Confirm the 1,000-point finish. A correct unique code awards exactly 1,000 points and freezes the score, history, and feedback until the next run.
Play the puzzle itself at Crack the Code to verify each step against the live clue rows and the keypad.
Scoring, Mistakes, and the 1,000-Point Finish
The score is deliberately simple. There is no speed bonus, clue multiplier, partial credit, and no penalty based on which wrong code was tried first. A correct code submitted on the very first guess and a correct code submitted after one distinct wrong guess both earn exactly 1,000 points. After a second distinct wrong code the run deadlocks and all submit actions freeze, so 1,000 points can only be earned on a run that finishes with at most one distinct wrong code.
The error budget is tight. A complete wrong code is recorded once. The first distinct wrong code remains repairable: clear the input or edit it and try another candidate. Submitting the identical wrong code a second time returns the same state reference and does not duplicate the history, consume the second error, or change feedback. A second distinct wrong complete code deadlocks the run. At that point the unique answer is disclosed and all digit, deletion, clearing, and submit actions freeze until you press Reset run. Completion is also terminal: entering 507 and submitting freezes the score, code, attempt history, and feedback.
Keyboard and Touch Input Rules
The interface is accessible without color. Clues state their counts in text, slots show either a digit or an underscore, distinct wrong codes are listed, and status copy gives both the number of used errors and the digits currently entered. All keypad buttons have native semantics and at least a touch-friendly minimum height, and the layout fits five columns inside a 390-pixel viewport without page overflow.
Digit buttons append from left to right until all three positions are filled. Physical keys 0 through 9 do the same. Backspace or Delete removes the final entered digit, Enter submits, and Clear guess empties only the current input. Reset run restores the entire game, including the attempt history and any terminal state. Incomplete input is safe. Submitting zero, one, or two digits reports how many positions remain but records no wrong attempt, which lets a keyboard or touch user correct an accidental early Enter without spending the finite error allowance. A fourth digit and any non-digit programmatic input are rejected atomically before they can affect the state, and the visible controls prevent both cases before submission. The shared double-Escape Boss Mode temporarily replaces the puzzle with a neutral spreadsheet view; returning from Boss Mode preserves the same code, wrong history, score, and terminal status.
Why Uniqueness Is Proven by Exhaustive Search
The product includes a pure scorer and a candidate enumerator, but the release test does not accept either as its own oracle. Instead it defines a separate literal clue table, implements its own exact removal and unmatched frequency maps, zero-pads every integer from 0 through 999, and filters all 1,000 candidates. That independent traversal returns only 507. The tests compare the production result against that one-element oracle set and also exercise the scoring boundaries shown in the table above.
State tests cover incomplete safety, first-error repair, identical-error atomicity, second-distinct-error deadlock, leading-zero entry, deletion, digit-cap enforcement, invalid-character rejection, full reset shape, exact score, and frozen terminal states. Each explicit behavior has a concrete assertion rather than relying on a visual impression, so the uniqueness of 507 is mechanical rather than asserted. Everything runs locally in the browser, no guess or score is uploaded, and the bundled fixture means the same clues and the same unique answer remain available offline after the page loads. Crack the Code is recreational entertainment, not an intelligence test, aptitude measure, classroom placement tool, hiring screen, health instrument, or psychological assessment, and the 1,000-point result is entertainment behavior rather than a standardized reasoning measurement. For an unaided solve, start with the displaced-only clue showing that 7, 5, and 0 are all present, then use the two exact positions in 527 to determine their order.