Chinese version 1: One rock two birds
yì shí èr niăo
一石二鸟
Chinese version 2: One arrow two hawks
yí jiàn shuāng diāo
一箭双雕
By giving a problem three thoughts, you can often come up with a solution crafty enough to take care of two birds at once.
In this Chinese chéng yŭ (成语), the language is cut down to the barest images. In the alternative saying, the birds are somewhat bigger and the act of shooting an arrow somewhat harder.
Perhaps we can assume that bigger problems must be expressed through bigger fowl?