Barge Problem: Acme Water Balloons — Meep Meep!

You have been hired by Acme Inc. to help test their new line of “Prankster Water Balloons.”
In particular, Acme wants to know the lowest height (in whole feet) from which their water balloons will burst when dropped. (They have already determined that their balloons all burst when dropped from 120 feet.) For example, if you had one balloon for testing you could drop the balloon from 1 foot; if it survives, drop it from 2 feet and continue upward until it breaks.

Acme, being pranksters themselves, only gives you two balloons for testing and will only pay you (in Acme Iron Anvils) if you determine this height in the fewest number of ballon-droppings possible.

What is the optimal strategy?

Solutions can be emailed to Professor Jonathan Bloom (bloomjs@lafayette.edu). Submissions are due by 6 a.m. on Saturday Sept. 28th.

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