Hi Zerghua, if you choose 3 first, then the possible number maybe in [1,2] or [4,6]. If it's in [1,2] interval, the minimum cost will be 3+1=4. If it's in [4,6], the minimum cost is 3+5=8. Here since 8 is greater then 4, we can promise 8 is sufficient.
To be short, if you suggest choosing 3 first, the formula should be 3+max(min[1,2],min[4,6]) instead of min[1,2]+3+min[4,6].
@zpcore Thanks for your explanation, that makes sense.