Contingencies Online - January/February 2013

And fourth, there are 81 pieces of metal that weigh 12, 22, 32…. 812. Can you divide them into three groups so that each group weighs the same amount?

busy times.

Thanks again to all who have played along with me, and thanks to Lenny for taking over. So long!

LENNY SHTEYMAN, a fellow of the society of actuaries, is an actuary with aXa equitable in new York.

previous Issue’s puzzle

Swan Song Solution

Mark Danburg-Wyld writes: What I enjoy about this puzzle is that while it seems very simple, when you start trying to solve it, there end up being an excess of possible approaches. Most solvers seemed to use the Pythagorean theorem, but similar triangles are another possibility: Let h be the height where they cross, L_ 1 the height where ladder 1 hits the wall, and L_ 2 the height where ladder 2 hits the wall. Then 1/L_ 1 + 1/L_ 2 = 1/h. This formula is better than a brute-force search for the second part of the puzzle.

The answer to Part 1 is 8.6445037309. For Part 2, if you put on the condition that the two ladders are of different lengths, the minimum total length of the two ladders is 70 meters in length for the first ladder and 119 meters for the second ladder. The alley width is 56, and the two ladders cross at a height of 30 meters. If you allow both ladders to be the same length, the minimum total length is when both ladders are five meters in length. In this case, the ladders cross two meters above the ground and the alley is three meters wide.

I would like to offer special recognition to Al Spooner and to Rui Guo, who have the distinction of having solved every puzzle I wrote over the past five years—a perfect record! Well done, Al and Rui. I never could stump you. Extra congratulations as well to Bob Byrne, Lee Michelson, and Robert Bartholomew, each of whom missed at most one month over the full five years, no doubt due to

Solvers

robert Bartholomew, Bob Byrne, Geoff
Bridges, Bill Carroll, Bob Conger, Mike
Crooks, Andrew Dean, Paul Dennee,
David engelmayer, Mark evans, rui
Guo, Jeff Larrimore, David Lovit,
Bob Maguire, James McGuire, Lee
Michelson, Geoff Moak, Tyson Mohr,
Paul navratil, Don onnen, Jeff Plank,
David Promislow, Colin Scheriff,
Craig Schmid, noam Segal, Tomasz
Serbinowski, Lenny Shteyman, John
Snyder, Don Sondergeld, Al Spooner,
Jon Turnes, Michael Vech, Daniel
Winnowski, ron yu

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