Chiu Chang Suann Jing/Examples/Example 2

Example of Problem from Chiu Chang Suann Jing

Suppose that there are a number of rabbits and pheasants confined in a cage,

in all thirty-five heads and ninety-four feet;

required the number of each?

Solution

There are $12$ rabbits and $23$ pheasants.

Proof

Let $r$ be the number of rabbits.

Let $p$ be the number of pheasants.

It is assumed that the rabbits all have $4$ feet and the pheasants $2$.

Then:

\(\text {(1)}: \quad\)

\(\ds r + p\)

\(=\)

\(\ds 35\)

\(\text {(2)}: \quad\)

\(\ds 4 r + 2 p\)

\(=\)

\(\ds 94\)

\(\text {(3)}: \quad\)

\(\ds \leadsto \ \ \)

\(\ds 2 r + 2 p\)

\(=\)

\(\ds 70\)

$(1) \times 2$

\(\ds \leadsto \ \ \)

\(\ds 2 r\)

\(=\)

\(\ds 24\)

$(2) - (3)$

\(\ds \leadsto \ \ \)

\(\ds r\)

\(=\)

\(\ds 12\)

\(\ds \leadsto \ \ \)

\(\ds p\)

\(=\)

\(\ds 35 - 12\)

\(\ds \)

\(=\)

\(\ds 23\)

$\blacksquare$

Sources

• c. 100: Anonymous: Chiu Chang Suann Jing
• 1965: Henrietta Midonick: The Treasury of Mathematics: Volume $\text { 1 }$
• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The Nine Chapters: $60$