02 / Mango numbers

Put every mango in its numbered place

A tiny board, a missing value and enough information to reason your way home.

The three-number mango crate

Every row and every column must contain 1, 2 and 3 exactly once. Diagonals do not matter. Fill the empty middle cell.

12321312

Count first, or place first?

Number puzzles can look alike while asking for very different actions. A basket question asks how many mangoes you have altogether. A placement board asks which symbol belongs in a particular position under a set of restrictions. The digits on this page are labels for placements; you do not need to add all nine cells to solve it.

Our daily challenge uses simple arithmetic. This crate uses a small Latin-square rule: each row and each column contains every allowed symbol once. Keeping those tasks separate is the first useful step. Before calculating anything, ask whether you are finding a quantity, completing a set or satisfying a positional rule.

Name the allowed set

The complete set here is 1, 2 and 3. Write those three candidates mentally or on paper before looking at the empty cell. The middle row already contains 2 and 1. Those values cannot be repeated within that row, so only 3 remains available. This is elimination rather than a guess based on appearance.

Now inspect the middle column. It contains 2 at the top and 1 at the bottom. Again, 3 is the missing member. Both directions point to the same answer. Entering 3 completes the board without requiring a trial run or a longer chain of deductions.

Check the whole rule, not just one part

A number can satisfy a row while conflicting with its column on a larger board. That is why checking both is a habit worth practising even when the example is tiny. The correct placement must meet all stated restrictions at once. A value that passes one test but fails another is not almost correct.

Notice what the instructions do not say. Diagonals are unrestricted. There are no smaller boxed regions, and the numbers do not have to form an arithmetic progression. Do not import extra rules from another puzzle just because the layout looks familiar. Sudoku, for example, has additional regional constraints that are absent here.

A useful number is not merely missing nearby. It must be allowed everywhere its placement has an effect.

When several candidates remain

Our starter board has just one blank, but you can make a paper version with several. Write the possible values beside each empty position. If a cell can hold either 1 or 3, leave both possibilities visible instead of forcing an early choice. Then examine a different row or column for a place with only one candidate.

After filling a confirmed value, revisit the intersecting row and column. A new placement may remove a possibility elsewhere. Keep provisional notes distinct from final entries. Otherwise, one unsupported assumption can quietly become the basis for several later moves, making the eventual contradiction difficult to trace.

Build a fair homemade crate

Start with the completed board shown here and cover a few cells with paper. Ask a friend to fill them while obeying the row and column rule. If two different completions work, the puzzle does not have a unique answer under those clues. That is a property of the setup, not a failure by the solver.

Restore a clue and test again. A fair beginner puzzle should make its intended rule explicit and provide enough information for the intended answer. You can replace the digits with Mango, Lime and Papaya and preserve the structure. The reasoning depends on distinct symbols, not on the arithmetic meaning of the digits.

Keep the daily challenge friendly

The homepage basket question changes with the UTC date. It saves your attempts and solved status in this browser when storage is available. It does not compare players, verify identities or publish a ranking. An attempt is simply an answer selection, not a judgement about your ability.

If you answer incorrectly, use the feedback and read the quantities again. If you solve it immediately, enjoy the small completion and move on. These are entertainment puzzles, not clinical tests or evidence of broad cognitive improvement. Clear reasoning and a pleasant break are enough of a reward.

Solution recap: the missing value is 3 because both its row and its column already contain 1 and 2.
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