My 9-year-old son had the following math problem to solve:
A truck can carry $200$kg or less. We have 8 different boxes with given weights:
$81$kg, $73$kg, $67$kg, $49$kg, $37$kg, $34$kg, $30$kg, and $26$kg
What is the minimum number of trip required to move all boxes from city A to city B.
I looked at it for 5 minutes and couldn't figure out a meaningful approach other than brute force.
I was in front of my computer and quickly wrote a MATLAB script to bruteforce it.
The solution was 2 trips: one with boxes $81$, $49$, and $67$; and the other with boxes $73$, $37$, $30$, $26$, and $34$.
Is there an obvious way, or at least one more clever than brute force, to solve that kind of problem?
Here, it's not that hard because we only have 8 boxes. But what about a similar problem with a bigger set? Can we only rely on brute force?
Bonus question:
What is this supposed to teach to a 9yo kid ?