### This Month's Contest: THE BEATLES

The Beatles are on a late night hike and they need to get through a dark tunnel as quickly as possible. They have only one flashlight. The band mates walk at different speeds. The tunnel is big enough for only two people at a time, and each pair has to walk at the speed of the slower walker. At least one person in the tunnel must have a flashlight. Here is how long it takes each Beatle to cross the tunnel:

 John 1 minute Paul 2 minutes George 5 minutes Ringo 10 minutes

What's the fastest time you can get John, Paul, George, and Ringo through the tunnel? You must provide the sequence you used. (Hint: Work the logic. Everything you need is here. It's not about finesses such as carrying another person on your back or throwing the flashlight back and forth.)

### Brainteaser #2: TEN ENVELOPES

The challenge is to distribute one thousand one-dollar bills in ten envelopes in such a way that no matter what dollar amount is called for, you can hand over some combination of envelopes and be assured of providing the requested amount for any figure from one dollar to one thousand dollars. See solution below.

### SOLUTION TO PREVIOUS PUZZLER: MOVING WALKWAY

To recap: Andy and Bob conduct an experiment with a moving walkway. Andy runs on the moving walkway while Bob runs alongside on the floor. Then they reverse direction. Who reaches the beginning of the moving walkway first, Bob or Andy, or will they finish at the same time?

Solution: Bob.

We received over 50 entries and since almost everyone figured out that Bob will always win, I gave extra points for the elegance of the explanation. The winner is Bradley R. Britton, UBS Financial Services, Inc., Salt Lake City, Utah, who wrote: “Bob will reach the beginning of the moving walkway first. This is because no matter how long the walkway is and no matter how fast the two run, Andy will be adversely impacted by the amount of time spent on the trip back. While Andy's average speed will be the same as Bob's average speed, Andy will spend more time at the slower speed and will always lose the race.” Congratulations to Brad Britton and good luck to all entrants for next time.

SOLUTION TO TEN ENVELOPS: The 10 envelopes have the following sums: \$1, \$2, \$4, \$8, \$16, \$32, \$64, \$128, \$256, \$489. Does the series look familiar? It should. It's the base two series: two raised to the power of one to nine. Two to the tenth is 512, but since you have only \$1,000, and the sum of the first nine envelopes is \$511, the last envelope is left with \$489. You can get any possible dollar amount between \$1 and \$511 by using the first nine envelopes. For dollar amounts higher than \$511, you can use \$489 plus a combination of the first nine envelopes.

John Kador is the author of 10 books. His latest book is Effective Apology: Mending Fences, Building Bridges, and Restoring Trust (Berrett-Koehler). www.effectiveapology.com.