A single correct equation starts a Mathoji puzzle; finding every distinct solution completes it. The useful question after a good answer is: which cases have I still not checked?
Start with the allowed choices
Standard puzzles use digits zero through nine in each blank. A digit may be repeated. Fixed numbers printed in the equation do not use up keypad choices. Master puzzles use their own displayed expression choices instead. Those limits are part of the puzzle, not optional hints.
List pairs in one order
For _ + _ = 5, keep the first blank no larger than the second. You obtain 0 + 5, 1 + 4 and 2 + 3. Continuing to 3 + 2 repeats the previous pair. The game accepts either order, but it counts the two orders once.
The same applies to multiplication. In a chain such as a × b × c, write factors in increasing order while searching. The triples 2, 5, 8 and 8, 2, 5 are one multiplication solution, so listing both does not bring you closer to completion.
Preserve the expression’s structure
Reordering terms within the same addition or multiplication is ignored. Brackets still matter. Swapping two whole bracketed sums in their product repeats a solution, but moving just one digit across those brackets can change their values. Subtraction and division keep their order: 9 − 0 is not interchangeable with 0 − 9.
Equal numerical totals alone do not make solutions duplicates. For example, √1 × 2 and √4 × 1 both equal two, but use different root-and-operand structures. In a suitable Master puzzle, both can earn a row.
Use a bound to prove you are finished
For _ × _ × _ − _ = 74, the product must be between seventy-four and eighty-three. That small range contains only three possible products made from three digit factors: seventy-five, eighty and eighty-one. Listing their unordered triples yields five answers. The range explains why other targets do not need testing.
Read the board as a record
Correct equations stay green. Use them to remember which cases you have completed. A duplicate message means the arrangement repeats a solved case; an invalid message means the equation or permitted choices failed a rule. Hints and Reveal can help, and assisted games remain marked as assisted in local performance.