# Feynman long division

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Here's a good example of a Feynman long division.

Dr. Richard P. Feynman posed the following puzzle: Each of the dots below represents some digit (any digit 0 to 9). Each of the \(A\)'s represents the same digit. None of the dots are the same as \(A.\)

What is the sum of the divisor, the dividend, and the quotient?

\(\)

**Details and Assumptions:**

- Both manual and CS solutions are encouraged.
- You can see the original letter below.

\[ \LARGE{
\require{enclose}
\begin{array}{rll}
\phantom{0}\ \mathrm{\large7} \ \mathrm{x} \ \mathrm{x} \ \mathrm{x} && \\[-1pt]
\mathrm{x} \ \mathrm{x} \ \mathrm{x} \

\enclose{longdiv}{
\mathrm{x} \ \mathrm{x} \ \mathrm{x} \ \mathrm{x} \ \mathrm{x} \ \mathrm{x} }\kern-.2ex \\[-1pt]
\underline{ \mathrm{x} \ \mathrm{x} \ \mathrm{x} \ \phantom 0 \ \phantom 0 \ \phantom 0 } \\[-1pt]
{ \mathrm{x} \ \mathrm{x} \ \mathrm{x} \ \mathrm{\large7} \ \phantom0 \ \phantom0 \ }\kern-.2ex \\[-1pt] \underline{ \mathrm{x} \ \mathrm{x} \ \mathrm{x} \ \mathrm{x} \ \phantom 0 \ \phantom 0 } && \\[-1pt]
{ \mathrm{x} \ \mathrm{x} \ \mathrm{x} \ \mathrm{x} }\kern-.2ex \\[-1pt]
\underline{ \mathrm{x} \ \mathrm{x} \ \mathrm{x} \ \mathrm{x} } && \\[-1pt] \mathrm{\large7}
\end{array} } \]

The above is a long division with most of the digits of any number hidden, except for the three 7's. Given that each of 0, 1, 2, ..., 9 was used at least once for the hidden digits, figure out all of the digits hiding and submit your answer as the value of the dividend (the 6-digit number being divided).

\(\)

**Details and Assumptions:**

- Each \(\mathrm X\) represents a single-digit integer.
- The leading (leftmost) digit of a number cannot be 0.

**Cite as:**Feynman long division.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/feynman-long-division/