# Sun Tzu Suan Ching/Examples

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## Examples of Problems from

## Examples of Problems from *Sun Tzu Suan Ching*

### Example $1$

*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."*

### Example $2$

*There are certain things whose number is unknown.**Repeatedly divided by $3$, the remainder is $2$;**by $5$ the remainder is $3$,**and by $7$ the remainder is $2$.*

*What will be the number?*

### Example $3$

*There are $3$ sisters, of whom the eldest comes home once every $5$ days,**the middle every $4$ days,**and the youngest in every $3$ days.*

*In how many days will all the $3$ meet together?*