What is the probability that a random five-digit zip code has five unique digits—that is, no digit appears more than once in the zip code?
Everyone with a mailing address in the U.S. has a five-digit zip code. Zip codes begin with 0 on the East Coast, and by the time they get to the West Coast they start with 9. My zip code—17889 (Winfield, Pa.)—has a repeating digit, so it doesn’t conform to the unique digit test. Assuming that zip codes are random five-digit numbers, what is the probability that any zip code consists of five unique digits?
Please email your solution to John Kador at [email protected] using the subject line “Zip Code Odds.” Deadline is Jan. 1, 2015. One entrant with the most compelling solution (or a creative alternative) will receive a signed copy of John Kador’s How to Ace the Brainteaser Job Interview. Good luck to all.
Solution to previous puzzler: WALK OR DRIVE
To recap: Would you rather have a penny for every step you will ever walk or a dollar for every mile you will ever drive?
Readers loved this puzzle and approached it in highly playful and creative ways. Everyone agreed that walking was by far the best deal, supporting their conclusions with a variety of assumptions. The winning entry—from Adam Roslovic, Maxwell Financial Management in New Albany, Ohio—is representative of the type of fun readers had with this puzzle. Can you tell that Adam is a Certified Financial Planner?
“Considering it costs approximately $.61/mile (per AAA, based on 15,000 miles/year, 2013), you are actually receiving $.39/mile from your dollar. So driving 2 hours/day at 30 mph = 60 miles/day * 5 days/week * 50 weeks/year (2 vacation weeks! - 15,000 miles/year) * 70 years (age 16 (I have to drive) to 86) = $409,500 … this is barring the dangers of autos and being allowed/able to drive into your late 80s!
“Per ‘about health’ website, a ‘contemporary man’ (the question states ‘Would you rather have…’ or ‘me’—a man) walks 7,192 steps/day. At 70 years of walking (age 2 to 72), it works out to $1.8MM. Therefore, I could take weekends off from walking, walk half of the estimate, retire to couch potato status at age 72, and still ‘win’ by almost $250k. Enough to cover the cost of a lifetime of nice shoes.”
Congratulations to Adam, and good luck to all in the current challenge.
For more of this month's Puzzler, check out Part 2.
John Kador is the author of 20 books. His latest book (with Brian Cohen) is What Every Angel Investor Wants You to Know: An Insider Reveals How to Get Smart Funding for Your Billion Dollar Idea (McGraw-Hill). www.jkador.com
