In the expression $$1□2□3□4$$ each $$□$$ is to be replaced by either $$+$$ or $$\times$$. What is the largest value of all the expressions that can be obtained in this way? 
Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
If $$m$$ and $$n$$ are positive integers, then $$mn{}\textgreater m+n$$ unless at least one of $$m$$ or $$n$$ is equal to $$1$$, or $$m=n=2$$. So, to maximise the expression, we need to place multiplication signs between $$2$$ and $$3$$ and between $$3$$ and $$4$$. However, we need to place an addition sign between $$1$$ and $$2$$ because $$1+2\times3\times4=25$$, whereas $$1\times2\times3\times4=24$$. 