Divisibility Detective Game

How to Play Divisibility Detective

One of the displayed integers is hidden. Read the revealed number-property clue and rule out any candidate that contradicts it. Activate a candidate only when you can explain why it fails. The game checks the mathematics of each elimination and gives a factorization, remainder or digit calculation. An integer that satisfies every revealed clue must remain available for now.

Select Check deductions after eliminating every contradicted candidate. The next clue then narrows the remaining list. Earlier clues stay visible, and each additional clue applies together with all previous clues. Continue until every other candidate is excluded and exactly one integer satisfies the complete set. The final check records that unique number as the answer.

The candidate board defines the search set: you are choosing from these displayed numbers, rather than from all integers. Easy uses short intervals with divisibility and digit clues. Normal uses larger candidates. Hard can also state the remainder left by division. Every generated clue is true of the hidden integer, and the complete clue set is verified to identify exactly one candidate.

Worked Deduction and Divisibility Rules

Suppose the candidates run from 20 through 39 and a clue says Divisible by 3. Their digit sums reveal that 21, 24, 27, 30, 33, 36 and 39 remain possible. A second clue saying Ones digit is 6 leaves only 36. It is divisible by 3 because 3 + 6 = 9, and its ones digit matches the second condition.

A number is divisible by 2 when its ones digit is even. Divisibility by 3 or 9 depends on the digit sum. A number divisible by 5 ends in 0 or 5, and a multiple of 10 ends in 0. Divisibility by 4 depends on the last two digits. You can also verify any displayed divisibility clue by calculating an exact quotient and checking for a zero remainder.

A negative clue such as Not divisible by 4 does not mean the candidate must be odd. For example, 18 satisfies that clue because 18 = 4 × 4 + 2. A remainder clue is more specific: a candidate must leave the stated remainder when divided by the named divisor. Do not discard an integer merely because it looks unlike another candidate; use an actual contradiction.

Controls, Daily Numbers and Records

Tap a candidate or reach its button with Tab and activate it with Enter or Space. Crossed candidates show an × and a strike-through. Activate a crossed candidate again to restore it, then recheck the deductions. Undo restores the previous elimination or clue stage and marks the round assisted. A hint gives one justified elimination or tells you when the stage is ready to check.

Daily mode gives the same candidate board and clues for a given UTC date and level. Practice mode offers another puzzle through New puzzle. The current clue stage, eliminated candidates and completed result save separately for each mode and level when browser storage is available. The shared practice calendar records a distinct completed puzzle only once.

There is no timer or typing-speed requirement. Incorrect choices reduce the possible score by five points, and each hint by fifteen, with a ten-point minimum for a completed round. Hints and Undo mark assistance, and assisted rounds do not replace an unaided best. Browser records stay local; if saving is unavailable, the deduction game still works during the current visit.

Frequently Asked Questions

Is the hidden number unique?

Yes. Within the displayed candidate set, exactly one integer satisfies all the generated clues.

Can I discard a candidate that still fits?

No. Each elimination must contradict at least one revealed clue.

Do previous clues still apply?

Yes. Every revealed clue applies together with all earlier clues.