Sun Tzu Suan Ching/Examples

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?