"Chickens and rabbits in the same cage" is a classical math problem proposed by 5th century Chinese mathematicians. The original question goes like this:
今有雉兔同籠上有三十五頭下九十四足問雉兔各幾何(There are pheasants and rabbits in the same cage, with 35 heads above, and 94 feet below. How many pheasants and rabbits are there respectively?)
At the time of this writing (Dec 2022), it seems that ChatGPT has trouble solving this type of problems. It often sets up the correct equations, but wanders into mistakes as it tries to solve the system. It also needs to be constantly reminded of the number of body parts each animal has. But it seems that with much patience, one can step-by-step, "hand-hold" it into finally giving the correct answer, for simple cases, that is.
This page generates more complex variations of the "chicken-bunny-cage" problem, involving more body parts and more animals, to challenge ChatGPT and see if it really "understands" the math, or is it merely mumbling math-sounding utterances?
The generated "reference" step-by-step solution uses Gauss-Jordan elimination underneath, and might be a bit too "robotic" for human taste.