Two mystery numbers multiply to 12 and add to 7 — find them. It is the puzzle hiding inside every factoring problem you have ever solved. The diamond problem (the 'x-box' or diamond method) is factoring made visual: write the product at the top of a diamond, the sum at the bottom, and find the two side numbers that multiply to the top and add to the bottom. For product 12 and sum 7, the numbers are 3 and 4 — which is exactly how you factor x² + 7x + 12 into (x + 3)(x + 4).

The method shines with negatives: product −10 and sum 3 gives 5 and −2, the pair behind x² + 3x − 10 = (x + 5)(x − 2). Algebra teachers across the US drill it because it turns guess-and-check factoring into a systematic hunt, and it doubles as integer puzzle practice. Enter the top and bottom numbers and the solver returns the side pair — or reports that no integer pair exists.

With the pre-filled defaults — Product (top) 12, Sum (bottom) 7 — the Diamond Problem Solver returns Number 1 (x₁) 4.0000, Number 2 (x₂) 3.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.