It's a Puzzlement

---

Interrupted Betting
by John P. Robertson

Tom Struppeck suggested this puzzle. In a best of seven series between evenly matched teams A and B, you have bet $100 on team A to win the series. Team A loses the first game, and you find you have to leave. You have an agent who will remain through the remainder of the series. This agent has some money of her own, and can place bets at even odds on each individual game, just before the start of each game. You give the agent some money, and instruct the agent on how to bet on each remaining game. The amount bet can vary from game to game, and can depend on the results to date of the series at the time of the bet. The goal of these bets is that the agent, after settling up on your behalf at the end of the series (collecting $100 if team A wins, or paying $100 if team B wins), will have broken even (i.e., she will have exactly as much money as she had before you gave her any money), and you will be out the amount of money you gave her. How much money do you give your agent, and how do you instruct her to bet?

Orienting Bottles

The goal is to put four bottles at the four corners of a rotating table into the same orientation, up or down, while blindfolded. You can only request that you be presented with two bottles that are in opposite corners or two bottles in adjacent corners (but you can't specify which corners).

Nicki Austin, Michael Dubin, Frank Karlinski, Alex Kozmin, David Uhland, and Dave Westerberg, found the following solution.

Call opposite and put both up.

Call adjacent and put both up.

If you have not won, then there is one down and three up.

Call opposite. If you get the one that is down, put it up, leave the other, and you've won.

If you get two up, turn one down, and leave other up.

Now you have two adjacent down and two adjacent up.

Call adjacent. If you get two in same orientation, turn both over, and be done.

If you get two in opposite orientation, turn both over.

Now you have opposites the same and adjacents different.

Call opposite and turn both over. Now you are done.