This Month's Contest:THE PRISON BREAK There are two cellmates locked in a prison cell. The guard will come in five hours to execute them. There is a window that is high up on the wall through which they could escape if they could reach it. The cell floor is made of dirt so they can tunnel. The only objects in their cell are a tin jug filled with water and a wooden bed, both of which can be repurposed
This Month's Contest:
THE PRISON BREAK
There are two cellmates locked in a prison cell. The guard will come in five hours to execute them. There is a window that is high up on the wall through which they could escape if they could reach it. The cell floor is made of dirt so they can tunnel. The only objects in their cell are a tin jug filled with water and a wooden bed, both of which can be repurposed in just one way: to make a rudimentary shovel. The executioner comes to the cell exactly five hours later and finds both men have escaped. How is this possible?
Here are the constraints:
- Even with one man standing on top of the other's shoulders, it is not possible to reach the window.
- They could dig their way out, but the tunnel would have to be 15 feet long, which would take them eight hours.
- They could move the bed under the window and stand on it, but they would still be six feet short of the window.
- Standing on the shoulders of one man standing on the bed, it might be possible for one to escape, but the other would be left behind.
In your pocket, you have 50 U.S. coins totaling exactly $1.00. A coin randomly falls out. What is the probability that the missing coin is a penny? See solution below.
How do they do it? Please e-mail your solution to John Kador at firstname.lastname@example.org using the subject line “Prison Break.” Deadline is April 1, 2012. One entrant with the correct answer (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: THE BEATLES
To recap: 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 that must accompany every trip. Only two bandmates can go through the tunnel at one time. The bandmates walk at different speeds (John 1 minute; Paul 2 minutes; George 5 minutes; Ringo 10 minutes). What's the fastest time the lads can get through the tunnel?
Solution: The minimum time is 17 minutes. The sequence is:
- John and Paul go through (2 minutes)
- Paul returns with the flashlight (2 minutes)
- George and Ringo go through (10 minutes)
- John returns with the flashlight (1 minute)
- John and Paul go through (2 minutes)
We had over 50 responses to the puzzle; 98 percent of them solved for 19 minutes, which is pretty good, but no cigar. Only a handful, like this issue's champion, found the optimum solution, 17 minutes. The winner is: J. Patrick Stites, district manager, Waddell & Reed, Franklin, Tenn. Congratulations to Patrick and good luck to all entrants for next time.
SOLUTION TO PENNY ODDS: There are two solutions: 80% if the coins do not include a quarter; 90% if the coins do include a quarter. Let n=nickels, d=dimes, q=quarters, and p=pennies. The simultaneous equations are 5n+p+10d+25q=100 and n+p+d+p=50. Subtract the two equations to get 4n+9d+24q=50. If you suppose q=0, then there are 0 quarters, 2 dimes, 8 nickels, and 40 pennies. That means the dropped coin has the probability of 40/50 or 80% to be a penny. If you suppose q=1, then there are 1 quarter, 2 dimes, 2 nickels, and 45 pennies. That means the probability is 45/50 or 90%. If you assume that the odds of having no quarters is the same as having one quarter, the average probability is 85%.
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.