Factorial and Power Digit
Equality Expressions Generator

How the equality works

The seed 12 supplies the digits on both sides. Its digits also supply the powers in a different order. The result 3 is not required to equal 12.

The search retains the digit order on each side and tests every parenthesization of adjacent terms. It allows addition, multiplication, subtraction of the second term, and subtraction of the first term. Negative intermediate values are permitted. The older script printed some negative expressions with incorrect arithmetic; this generator evaluates the expressions exactly before reporting them. No division is used.

Seven verified examples

These are the supplied identities. Each button searches the matching digit seed and result.

Choose result values

Set the interval for the value of both expressions. Leave the digit seed blank to try selected digit sequences automatically, including repeated digits.

Automatic search uses nonzero digits 1–9, including repetitions. Searching 2–4 digits with both limits set to all is exhaustive. Five and six digits have far more combinations: these modes require a limit of 1–100 equalities per sequence and a total limit of 1–5,000, so their results are partial. Choose “5 digits only” or “6 digits only” to reach those lengths without searching shorter sequences first. A single digit seed may have 2–6 digits. The result interval is inclusive. TXT and Excel include all found rows; the screen shows the first 200.