You think that $20 is likely to be the minimum, but it might not be enough. You know that $100 is certain to work but probably, you could get away with less. Perhaps $85, or maybe $70 — it’s hard to imagine until you try. So, you (maybe with the help of some of your friends) submit a sequence of envelopes containing integer amounts of dollars, and measure the effect. Say the first envelope contained $75. If the bribe was successful, you would know that the lower limit is between $20 and $75; however if there was no effect, you would know that the lower limit is between $76 and $100. And of course, like all attempted bribes, you won’t get back the $75. Devise an algorithm to determine the minimum effective bribe, by using an optimal strategy that uses the smallest total amount of your cash, in the worst case.