See Inside

# May 2003 Puzzle Solution [Preview]

When the possible offers are \$1 and \$5, the best strategy is to take the first 50 offers no matter what and then take only \$5 offers. If the ticket exchanger offers \$1 for each of your tickets and then halts the trading, your regret ratio would be 1.8 (\$90 divided by \$50). If the exchanger initially offers \$1 but then switches to \$5, the regret ratio would still be 1.8 (\$450 divided by \$250). If the possible offers are \$1 and \$1 million, take the first 45 offers no matter what and then wait for \$1-million offers. This strategy yields a regret ratio of 2.

The basic strategy is to take the first x offers no matter what they are and then take only \$5 offers after that. We are told that the number of tickets is 90, but let¿s solve this symbolically for a number T and then specialize to T = 90. If all offers are \$1, the oracle will get \$T, so the regret ratio will be T/x. If there are at least T \$5 offers, but they come after the first x have been given out, then the oracle will get \$5T, making the regret ratio 5T/(x + 5(T ¿ x)).

Subscribe     Buy This Issue

Already a Digital subscriber? Sign-in Now
If your institution has site license access, enter here.

### Add a Comment

You must sign in or register as a ScientificAmerican.com member to submit a comment.
Click one of the buttons below to register using an existing Social Account.

## More from Scientific American

• Octopus Chronicles | 9 hours ago

### Octopus In Space: Why the Latest U.S. Spy Rocket Is More Appropriate Than the NRO Knows

• TechMediaNetwork | 9 hours ago | 5

### Radiation on Mars 'Manageable' for Manned Mission, Curiosity Rover Reveals

• News | 9 hours ago | 2

### Powder Rive Basin Coal on the Move

• TechMediaNetwork | 9 hours ago | 1

### Formula 1 Racing Loud Enough to Damage Hearing

• News | 11 hours ago | 1

### Strategies for Aging Vary Widely across 46 Species with Some Scarcely Deteriorating

See what we're tweeting about

More »

## Latest from SA Blog Network

• ### Octopus In Space: Why the Latest U.S. Spy Rocket Is More Appropriate Than the NRO Knows

STAFF
Octopus Chronicles | 9 hours ago
• ### Oh the Horror! Best of the Blogs for November...

Video of the Week | 12 hours ago
• ### Best of the Blogs for November: Oh the Horror!!

PsiVid | 12 hours ago
• ### 4 Billion Years of Martian History in 2 Minutes

Life, Unbounded | 13 hours ago
• ### My Story Collider Story - Working Twice as Hard

The Urban Scientist | 14 hours ago

## Science Jobs of the Week

May 2003 Puzzle Solution: Scientific American Magazine

X

### Give a Gift & Get a Gift - Free!

Give a 1 year subscription as low as \$14.99

X

X

###### Welcome, . Do you have an existing ScientificAmerican.com account?

Yes, please link my existing account with for quick, secure access.

No, I would like to create a new account with my profile information.

X

Are you sure?

X

### Institutional Access

It has been identified that the institution you are trying to access this article from has institutional site license access to Scientific American on nature.com. To access this article in its entirety through site license access, click below.

X

X