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...The application generates arbitrary equations containing 1-4 variables. It is for the student to provide values for these variables which make the equation true. For example, in the screenshot above the equation is: 18-64-c*d=4. The student must choose values for c and d which result in a true statement. One approach would be to solve for the product "c*d" and then choose 2 numbers whose product satisfies what's needed. Like this: 18-64-c*d=4 18-64-4=c*d c*d=-50 Then the student could pick any two numbers with product of -50, like c=-25 and d=2. ...

...Draw a binary integer from a cell going upright, then explore the allowed transforms which may lead you to a factored state in 2 dimensions, from the lowest digit of the 2 odd integers both upright and upleft, its factors, and in the 2d space they are rectangle edges of, those pixels/digitbits must be on when there is an on bit somewhere downleft and downright after crossing empty cells, but if it finds either whole diagonal row empty then it must also be empty/zerodigit. The 2 main rules are: Any 2 cells below may both turn off and turn on the one above, or the reverse, and any on cell may move horizontally to an empty cell.