War of Attrition

The Blue Army and the Red Army commence fighting and continue, without reinforcements or replacements, until one side is completely annihilated. At any given instant after fighting begins the deterministic and continuous rate at which members of one army are “eliminated” is equal to the other army’s “firepower constant,” a positive number, times the surviving size of the other army at that time. For example, if the Red Army’s firepower constant is 0.0001 per second and the size of the Red Army three hours after fighting began is 800 members, then 0.08 members of the Blue Army are eliminated per second at that time. As it happens, the Blue Army wins while losing only 15% of its initial size. That is to say, 85% of the Blue Army survives and 0% of the Red Army survives. What would the outcome have been if the firepower constant of the Red Army had been tripled? What would the outcome have been if the initial size of the Red Army had been tripled?

Know the answer? Send your solution to ar@casact.org.

Paranormal Logic

This puzzle, which appeared in the July/August issue, listed six logical constraints on the existence of people who might have been abducted by a UFO, seen Bigfoot, seen Elvis last year, and might be able to levitate, produce cold fusion, and/or have ESP. The best way to see all possible types of people who might exist under these constraints is through the following Venn diagram representation of the constraints, constructed with some assistance from John Robertson.

The first question was whether it is possible that there are people who have been abducted by a UFO and can levitate but have not seen Bigfoot and cannot produce cold fusion. Yes, clearly there is an area for such people in the diagram. The second question was could anyone who has seen Bigfoot produce cold fusion. No, as there is no such area in the diagram.

Solutions were submitted by Bob Conger, Peter DeVries, Mario DiCaro, Stephanie Magnuson Jackson, John Jansen,Hana Jin, Jim Muza, Brad Rosin, and Dan Schobel.

AR Puzzle Editor Jon Evans is president of Convergent Actuarial Services, Inc. in Delray Beach, Florida.

Solution to “Celebrate Good Times! A Centennial Puzzle,” AR September/October 2014.