Sun Tzu Suan Ching/Examples

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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?