### THIS MONTH'S CONTEST

PADLOCK PROBLEM

Andy and Bob are associates at a large brokerage with offices in different cities. Andy needs to send a highly sensitive document to Bob, for only Bob to see. Andy has a number of padlocks with corresponding keys and a portable safe with a large clasp that can be secured by one or more padlocks. Bob does not have keys to any of the padlocks. The messenger will faithfully deliver the safe but cannot be trusted to respect the confidentiality of the safe's contents; if he can open the box in transit, he will. How can Andy securely send the document so that Bob and only Bob will see it?

Hint to readers: Work on the solution, not the problem. Everything you need to solve the problem is in the problem statement. It's not in the spirit of these puzzles to suggest, for example, that Andy can FedEx a key.

Please email your solution to John Kador ([email protected]) using the subject line “Equity Pairs.” The deadline is March 15, 2009. Two accurate responses, based on originality and creativity, will be selected to receive a signed copy of John Kador's *How to Ace the Brainteaser Job Interview*. Good luck.

### BRAINTEASER #2: HOURGLASS TIMING

You have two hourglasses. Hourglass one times exactly 7 minutes; hourglass two times exactly 11 minutes. Using just these two hourglasses and nothing else, how would you accurately time 15 minutes? Solution at bottom.

### SOLUTION TO PREVIOUS PUZZLER: FIVE EQUITIES

**To recap:** A broker instructs his assistant to select five equities for a client's portfolio and to make a note of the price of each. Instead of pricing the equities individually, the assistant combines the equities in pairs and gives the broker the sums of the values of these pairings: $20, $22, $23, $24, $25, $26, $27, $28, $30, $31. What are the dollar values of the five individual equities?

**Solution:** From the lowest value to highest: $9, $11, $13, $14, and $17.

Of the 35 entries we received, a majority got it right. There are many ways to arrive at the right answer, from trial and error to algebra. Below are examples of each. Congratulations to our two winners.

**Anthony Cornish**, financial advisor, Edward Jones, Ypsilanti, Mich: To figure this out I wrote out all the numbers in a row 1 through 31. I noticed that I could not have more than one number selected from numbers 15 through 31 because it would add up to too much. I also could not have more than one number selected from numbers 1-10 because it would add up to too little. This left me with numbers 11, 12, 13, and 14. I had to select 3 of these four. 9 from the low numbers and 17 from the high numbers were the only two to match up with the center four except 12. So, I ruled 12 out and my remaining numbers were 9, 11, 13, 14, and 17

**Robert Iannarelli**, President, Iannarelli Consulting, Ontario, Canada. Iannarelli set up equations to solve the problem: Let the five equity prices be: A, B, C, D, E. From the pairings we know that: The two lowest add up to 20, A+B = 20 (lowest pairing). The lowest and the middle price add up to 22, A+C = 22 (2nd lowest pairing). The two highest add up to 31, D+E = 31 (highest pairing). The highest and the middle price add up to 30, C+E= 30 (2nd highest pairing). The pairings include each equity 4 times: i.e.: A+B, A+C, A+D, A+E etc… The pairings add up to 256, therefore A+B+C+D+E = 256 / 4 = 64. Since A+B = 20, and D+E = 31, we can calculate C= 64-20-31= 13. A+C= 22, therefore A = 9. A+B = 20, therefore B = 11. C+E = 30, therefore E = 17. And finally, D+E = 31, therefore D =14.

**SOLUTION TO HOURGLASS TIMING:** Start both hourglasses simultaneously. At the end of seven minutes, flip over the seven minute hourglass. At this point four minutes remains in the 11-minute hourglass. When the 11-minute hourglass is empty, 4 minutes will have elapsed from the 7 minute-hourglass. Now flip the 7-minute hourglass over. When this hourglass is empty, you will have timed 15 minutes. (4+4+7=15.)