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Lizely

Math Crossword

Fill four shared variables so three crossing multiplication equations are simultaneously true.

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How to use

  1. 1.Move among A, B, C, and D with Left and Right; press 1 through 9 to enter a value.
  2. 2.Make 2 × A = B, A × C = D, and B × C = 12 agree at the same time.
  3. 3.Enter A=3, B=6, C=2, and D=6 cleanly to finish with 960 points.

About Math Crossword

Math Crossword is a compact multiplication consistency puzzle with four shared variables named A, B, C, and D. Fill one digit in each slot so all three displayed equations are true at the same time: 2 × A = B, A × C = D, and B × C = 12.

This is a fully disclosed Lizely product fixture based on the pipeline's multiplication-equation concept. It does not claim a published crossword standard and does not embed an external multiplication table. The arithmetic, variable sharing, accepted range, contradiction rule, controls, and score are all defined on the page and independently tested.

Move the visible selection left or right with the arrow keys. Press a number from 1 through 9 to replace the selected variable. Backspace or Delete clears it. Mouse and touch users can click a variable to cycle through the same one-digit range. The equation display repeats the current shared value, but each variable has only one editable button.

The clean solution is A = 3, B = 6, C = 2, and D = 6. Substitution gives 2 × 3 = 6, 3 × 2 = 6, and 6 × 2 = 12. Entering those four values once completes the puzzle in four actions and scores 960 from the initial 1,000.

Validation is incremental. An equation is checked only when every variable needed by that equation has a nonzero value. This avoids calling a partially filled but still repairable board wrong. As soon as a completed equation is false, the status reports a contradiction. Unlike a maze cul-de-sac, this mathematical deadlock is correctable by replacing a value.

For example, A = 4 and B = 8 satisfies the first equation and remains viable while C and D are empty. Changing A to 3 while B stays 8 immediately contradicts 2 × A = B. Restoring A to 4 clears the warning, proving that validation reflects the current board rather than permanently locking a mistaken input.

Completion requires four nonzero integer digits and all three equations true. Values outside 0 through 9, nonintegers, and arrays with the wrong shape are rejected by the pure logic boundary. The browser UI only offers the narrower 1 through 9 input plus zero as the clear state.

The independent test asserts the four-entry 960-point completion, wrong first equation, wrong shared-product equation, invalid board shape, a viable partial assignment, a newly introduced contradiction, and recovery after correction. This demonstrates both the golden route and the error path without deriving expected values from the UI.

The interface uses semantic buttons and text equations styled with site CSS variables. Each button announces the variable label, current value, and keyboard selection. There is no canvas, random generation, timer, audio, account, download, hardware access, network request, or pointer-only requirement.

Restart clears A through D, restores the first selection and 1,000 points, and removes every warning. The completed best score stays only in localStorage. Double-press Escape for the simulated spreadsheet boss screen and repeat it to resume the same puzzle. For related number play, try Addition Maze, Magic Square, Number Sequence Quiz, or Number Match 10.

Methodology & sources

The validator accepts exactly four integer slots from 0 through 9. It conditionally checks 2A=B, AC=D, and BC=12 once each equation's variables are nonzero. Any completed false equation sets deadlocked; all four values plus three true equations set complete. Score is max(0, 1000 minus 10 times edits).

Frequently asked questions

Why can the same value appear twice?
Variables must satisfy the equations; they are not required to be unique. In the solution, B and D both equal 6.
When does the contradiction warning appear?
Only after every variable used by an equation is filled and that complete equation is false.
Can I correct a contradictory board?
Yes. Replace or clear any variable; validation recalculates all three equations immediately.
How is the score calculated?
The game starts at 1,000 and subtracts 10 for each variable edit. Four clean entries score 960.

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