I have some problems finding out the answers为什么只能用finding而不能

have problems (in) doing something 是固定搭配,前面省略了介词in,介词后面只能跟动词的ing形式.
类似的还有：
have trouble / difficulty (in) doing sth.做某事有困难
have no problem (in) doing sth.做某事没困难,做某事没问题
have no trouble / difficulty (in) doing sth.
不能 have problems (in) doing sth 固定句型