101. From three barrels of rice of the same capacity, a certain amount of rice was stolen by three thieves. The total amount was unknown, but it was found that 1 go of rice remained in the first barrel, 1 shing 4 go in the second, and 1 go in the third. The captured thieves confessed: the first that he had scooped rice from the first barrel with a shovel, the second that he had used a wooden shoe, and the third a bowl, taking from the second and third barrels respectively. The shovel, shoe, and bowl were found at the scene of the crime. Upon measurement, it was found that the capacity of the shovel was 1 shing 9 go, the shoe 1 shing 7 go, and the bowl 1 shing 2 go.

It is required to find out how much each thief stole. It is known that 10 go = 1 shing; 10 shing = 1 tau; 10 tau = 1 shi.

From the treatise "The Beginnings of the Art of Calculation."

1(2. Find a number that, when divided by 3, gives a remainder of 2, when divided by 5 gives a remainder of 3, and when divided by 7 again gives a remainder of 2.
101. From the conditions of the problem, it follows that

$$
19 x+1=17 y+14=12 z+1
$$

where $x$ is the number of times rice was scooped with a shovel,

$y$ is the number of times with a shoe,

$\boldsymbol{z}$ is the number of times with a bowl.

Since $19 x=12 z$, then $x=\frac{12 z}{19}; x, y$ and $z$ must be integers. Therefore, we can assume that $z=19$, from which we obtain the indeterminate equation with two unknowns $17 y+13=$ $=228 u$. The smallest value of $u$ for which $y$ is an integer is $u=14; x=168; y=187; z=266$

| 1st thief. | 3 shi | 1 | tau 9 shing | 2nd |  |  |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 2nd | 3 | shi | 1 | tau | 7 shing | 9th |
| 3rd | p | 3 shi | 1 | tau | 9 shing | 2nd. |

In each box there was 3 shi 1 tau 9 shing of the 3rd.

The treatise "The Beginnings of the Art of Calculation" was printed in 1593.

It contains a number of articles and problems on arithmetic, geometry, and algebra, many of which are borrowed from "Jiu Zhang".