If the sequence of 5 positive integers (a,b,c,d,e) satisfy: $$abcde\leq {a+b+c+d+e} \leq 10m$$ then find the sum of digits of m.
I don't know how to approach this question. I know it's not a good way to ask here, but, if you may give any hint regarding this for the approach only, I will try my best to use it and apply.
Thank you.
This is the question. And its answer is given as 9. I don't know how?
Hint: Presumably $m$ must be the minimum value that makes the right inequality true. Unless some of $a,b,c,d,e$ are $1$, the product will be too large for the left inequality to hold. Even if one of them is $1$, the product will be at least $16$ and that will be too large. Work on justifying how small the sum must be.
If you are willing to count on the problem setter to have made sure there is a unique solution, you can just observe that $a=b=c=d=e=1$ allows $m=1$, assert that the sum of digits of $m$ must be $1$, and declare victory. Really you should prove that any $a,b,c,d,e$ that satisfies the left must allow $m=1$
Note that $a=b=c=d=1$ allows $e$ to be anything, which means we can force the minimum $m$ to be as large as we want. The problem is badly flawed.