Inverse Operation Trace Game
Reverse multi-step calculations to recover the original unknown value.
Choose Practice or Daily to begin.
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Instructions, device progress and accessibility
Choose Easy, Normal or Hard and select Practice or a daily puzzle based on the UTC date. Enter answers or choose a correction, then select Check answer. Hints and Undo mark a round as assisted. Best scores and progress are stored only in this browser; no account is needed.
Local progress is checked when play begins.
How to play Inverse Operation Trace
Begin at the final output shown on the right, and undo each operation from right to left. Enter the intermediate values and the starting x. Hard mode introduces a third operation.
Worked example
Example: x → ×3 → +5 → 20. First subtract 5 from 20 to get 15, then divide by 3 to recover x = 5.
Math formulas and key skills
Inverse pairs: +a reverses −a; ×a reverses ÷a (a ≠ 0). Reverse the operations in the opposite order to the original path.
Avoid common mistakes
Do not run the arrows from left to right when solving backward; undo the last operation first, then the earlier steps.
Frequently asked questions
What is an inverse operation?
It is an operation that reverses another operation, such as subtracting 4 to undo adding 4.
Why do inverse operations help solve equations?
They isolate the unknown by reversing the arithmetic performed on it, one step at a time.