Am I completely misunderstanding the problem, or is the math in the example solution wrong?

    Bursting 1 first gives you 3×1×5=15 coins. <-- OK...
    Bursting 3 first gives you 1×3×1=1 coins. (using left virtual balloon) <-- Should be 3?
    A possibility would be bursting 1, then 5, then 3, which gives you a total of 3×1×5+3×5×1+1×3×1=33 coins. <-- Should be 3x1x5+1x5x1+1x3x1=24?

  3 1 5 -> pop 1 = 15
  3 _ 5 -> pop 3 = 3

  3 1 5 -> pop 1 = 15
  3 5   -> pop 3 = 15

This is fairly old Leetcode problem (who probably got it from somewhere else)

https://leetcode.com/problems/burst-balloons/description/

Its tricky and if I got this problem in a tech interview, I would be hard-pressed to solve it in 45 minutes if I hadn't seen it before

this would really be helped by demonstrating the wrong way to solve this, which is trying to think of the first balloon in the range and then combine with the subproblems. i expect this to be where people who know about dp are most likely to get hung up, and may not realize they can think about it the opposite way.