# Sun Tzu Suan Ching/Examples/Example 1

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## Example of Problem from

## Example of Problem from *Sun Tzu Suan Ching*

*A woman was washing dishes in a river, when an official whose business was overseeing the waters demanded of her:**"Why are there so many dishes here?"*

*"Because a feasting was entertained in the house," the woman replied.**Thereuon the official enquired the number of guests.*

*"I don't know," the woman said, "how many guests there had been;**but every $2$ used a dish for rice between them;**every $3$ a dish for broth;**every $4$ a dish for meat;**and there were $65$ dishes in all."*

## Solution

- $60$ guests.

## Proof

Let $x$ be the number of guests.

Then:

\(\ds \dfrac x 2 + \dfrac x 3 + \dfrac x 4\) | \(=\) | \(\ds 65\) | ||||||||||||

\(\ds 13 x\) | \(=\) | \(\ds 780\) | multiplying through by $12$ and simplifying | |||||||||||

\(\ds x\) | \(=\) | \(\ds 60\) |

$\blacksquare$

## Sources

- c. 280 -- 473: Sun Tzu:
*Sun Tzu Suan Ching* - 1913: Yoshio Mikami:
*The Development of Mathematics in China and Japan* - 1992: David Wells:
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