If you buy all the most expensive balls, that is, all the big balls from 25 yuan, you need to spend 42*25= 1050 yuan, but in fact you only spent 882 yuan, which means you didn't buy all the big balls. The difference between a big ball and a small ball is 25- 18=7 yuan, so divide the difference by 1050-882= 168 yuan, and the formula is 168/7=24, which means you bought a small ball. So 42-24= 18, which means you bought a big ball of 18. This is done by the gap method. The principle is to assume that the difference between buying all the big balls and the actual cost is actually the difference between buying more big balls and small balls. By division, we can quickly find out the number of big balls bought. This problem is 18 big ball and 24 small balls. Finally, you can check: 18*25+24* 18=882 yuan.