An empty shape does not count as a mistake in Fraction Shape Puzzle. Pressing Check shape with zero cells shaded produces an "incomplete" message, leaves your score unchanged, and does not add to your distinct-error counter, so the run keeps moving and you can keep shading cells on the same card. A mistake is only logged when you submit a non-empty shaded pattern whose cross product does not match the target fraction, and a second, different wrong pattern is what closes the run. The question "does an empty shape count as a mistake" therefore has a precise answer: it counts as nothing, because the game treats an empty submission as not-yet-attempted rather than wrong, the same way a blank answer on a paper test would be left blank rather than marked incorrect. You get the same feedback regardless of which of the five cards you try it on, and you can re-check after every shading change without burning a turn.
This empty submission rule matters because the rest of the game is built around a strict two-mistake cap. Fraction Shape Puzzle awards 200 points for every correct card and ends a run after a second distinct wrong shaded pattern on any level, which is why understanding exactly when a mistake gets recorded protects your score. The official browser version at Fraction Shape Puzzle displays the current shaded fraction, the target fraction, the cross products after a valid check, your distinct errors, and your score on a single status strip, so the answer to the empty-shape question is visible on screen rather than hidden in a rulebook.
How the Mistake Counter Behaves in Fraction Shape Puzzle
The mistake counter is bound to a level-and-shaded-mask signature, which is the technical term for "which card you are on plus exactly which cells are currently shaded." Two submissions count as the same mistake only if they come from the same level and produce the same set of shaded cell indexes; any other combination is a different signature and therefore a different mistake.
- Empty shape on any card. The check runs, an incomplete message appears, and nothing changes. The score stays the same and the distinct-errors counter stays at zero.
- First wrong non-empty shading on any card. The cross products do not match, the first distinct mistake is logged, and you can keep shading and rechecking.
- Same wrong shading resubmitted on the same card. The signature is identical, the mistake is not duplicated, and the distinct-errors counter does not move.
- Second distinct wrong shading on the same or another card. The second mistake is logged, the run freezes all cell toggles, cursor movement, and checks, and you have to restart to play again.
That four-row description is the full mistake lifecycle, and it is what guarantees that pressing Check shape while you are still thinking, or while you are correcting an earlier mistake, never counts against you.
How to Play Fraction Shape Puzzle Step by Step
The controls and the order of actions are fixed, so the safest way to use the empty-submission rule is to follow the same workflow on every card.
- Read the target fraction in the upper display and count the equal cells drawn inside the rectangle, because the target's denominator does not match the count of equal parts in the shape, which is why the game uses cross products to test equivalence rather than comparing the two numbers directly.
- Pick the cells you want to shade using the visible cell buttons with a pointer or touch screen, or move a cursor with the Arrow keys and press Space to toggle shading on the active cell.
- Press Check shape, either by clicking the on-screen button or by pressing C on the keyboard, to compare shadedCount × targetDenominator against targetNumerator × partCount.
- Read the two cross products that the game prints below the current shaded fraction; equal numbers mean a correct card worth 200 points, unequal numbers mean a mistake unless the shape was empty.
- Advance to the next fixed card, repeat the same workflow for all five targets, and finish the run at exactly 1,000 points with zero distinct mistakes for a clean scoreboard.
If your first check is wrong, the run does not end. You can keep shading different cells until either your cross products match and you score the 200 points, or you produce a second distinct wrong shading and the run freezes on the second distinct mistake.
Empty Shape vs Non-Empty Wrong Shape: What's the Difference
The distinction between an empty shape and a non-empty wrong shape is the entire reason the rule exists, so it helps to compare them side by side.
| Action | What the game does | Effect on score | Effect on distinct errors |
|---|---|---|---|
| Check shape with zero shaded cells | Shows "incomplete" feedback | No change | No change |
| Check shape with a non-matching pattern | Shows the unequal cross products | No change | +1 distinct mistake |
| Recheck the same non-matching pattern | Recognizes the identical signature | No change | No change |
| Check shape with a second non-matching pattern | Logs a new signature | No change | +1 distinct mistake; run freezes on the second |
| Check shape with a matching pattern | Shows equal cross products | +200 points | No change; advances to the next card |
The middle row is the one that gets confused with the first row, because both produce feedback that says you have not succeeded. The first row just means "you haven't tried yet," while the second row means "you've tried, and the math didn't line up." Knowing the difference is what lets you experiment freely without burning a turn.
The Five Fixed Cards and Their Cross Products
Every Fraction Shape Puzzle run presents the same five cards in the same order, which makes the right shaded counts easy to verify on paper before you press Check shape.
| Card | Equal cells | Target fraction | Cells to shade | Cross product check |
|---|---|---|---|---|
| 1 | 4 | 1/2 | 2 | 2 × 2 = 1 × 4 = 4 |
| 2 | 6 | 2/3 | 4 | 4 × 3 = 2 × 6 = 12 |
| 3 | 8 | 3/4 | 6 | 6 × 4 = 3 × 8 = 24 |
| 4 | 10 | 2/5 | 4 | 4 × 5 = 2 × 10 = 20 |
| 5 | 12 | 5/6 | 10 | 10 × 6 = 5 × 12 = 60 |
Each row is one card, and each cross product is a tiny multiplication you can do in your head before committing. Card 3 is a useful one to walk through in detail because it combines a denominator higher than the target and a numerator that does not match the cell count. With eight equal parts and a target of three quarters, the shaded count is six. The game computes shadedCount × targetDenominator, which is 6 × 4 = 24, and targetNumerator × partCount, which is 3 × 8 = 24. Because both products equal 24, the card is accepted and the 200 points are added; shade a seventh cell and the products become 7 × 4 = 28 against 3 × 8 = 24, the signature is recorded as a wrong mask, and you have used one of your two available mistakes on a single card.
Why the Game Uses Cross Products Instead of Decimals
Fraction equivalence can be tricky because two fractions that look different can describe the same share of a whole. If the game converted shaded counts to decimals, one half and five tenths would both render as 0.5, which works, but three quarters and seven tenths would render as 0.75 and 0.7 and would only be judged different because of the way decimal expansions terminate. Many other equivalents would round to misleading values.
The cross product test sidesteps that whole class of bugs by staying in the integers. The check shadedCount × targetDenominator = targetNumerator × partCount is exactly the test recommended for verifying equivalent fractions without reducing them first, and it is the test you saw in the five-card table. The cross product test decides whether a given masked shape is correct, while the dedup rule separately keys on the exact level-and-shaded-mask signature, so resubmitting the identical set of shaded cells counts as one mistake rather than two; two different masks that happen to yield the same equivalence are different signatures and would count as different mistakes. For a side-by-side walkthrough of how the five cards map to their cross products, see the Fraction Shapes Game: Match 5 Targets With Cross Products guide.
What the Sources Cover and What They Don't Cover
The fraction rules behind the game come from two openly available mathematics sources. The visual equal-parts model that defines a fraction as numerator counts of denominator parts is described in OpenStax Prealgebra, section 4.1 on visualizing fractions, and the cross product test for equivalence is described in the LibreTexts chapter on equivalent fractions. The game uses both: OpenStax for the visual shape, and LibreTexts for the integer-based equivalence check.
It is worth being explicit about what those sources do not endorse, because the literature covers fraction rules but not gameplay choices. The cited sources support fraction visualization and equivalence only, and they do not endorse the game's specific five-card selection, the 200-points-per-card scoring, the empty-shape rule, or the distinct-mistake cap. Those parts of the design are product choices inside the game itself, not claims about mathematics.
Edge Cases the Game Handles Automatically
A few edge cases are worth knowing because they are the only ways the inputs to the game can break. The game rejects a zero target denominator, an impossible part count, and any unsafe cross-product boundary before it tries to score the card, so a card will not silently award zero points for nonsense input. Negative, fractional, or out-of-range cell indexes are atomic no-ops, which means an out-of-bounds keypress simply does nothing and the cursor stays put.
Once the run is complete or deadlocked, cell toggles, cursor movement, and Check shape are all frozen, and a restart returns you to card one, an empty shape, zero points, and zero mistakes. All state stays inside your browser, which is why there is nothing to save, nothing to upload, and nothing to time out. The interface shows enough of the math (both sides of the cross products, the current shaded fraction, the target fraction, the level progress, distinct errors, feedback, and score) for every decision to be auditable on screen.
For a deeper look, see Hidato Daily Puzzle: Solve a Fixed 4x4 Number Path.