It's a Puzzlement
Babies - A Pink or Blue Addition Problem

by John Robertson

A nurse has just started to count the babies in a hospital nursery. He has just counted that there are two boys, and has not counted the girls, when, at 11:00, a new baby is brought in to the nursery. A baby is then selected at random, from all the babies present, to have its footprint taken. The selected baby happens to be a boy. What is the probability that the baby added at 11:00 was a girl?

The Snowplow

This puzzlement had snow falling at a steady rate. A snowplow started at 6:00 A.M., drove in a straight line, and removed snow at a constant rate (in cubic feet per minute). In particular, the deeper the snow got, the slower the snowplow went. The plow went twice as far in the first hour as in the second hour. The question was, when had it started to snow?

Mitch Pollack submitted the correct solution. It began to snow at about 5.382, or 5:23 AM. E-mail the CAS Office for the complete solution.

Solutions were also sent in by Donald Behan, Alex Bondarev, Jeff Eddinger, Chuck Emma, Walter Fransen, Kevin Hobbs, Ignace Kuchazik, Andy Minten, Melissa Neidlinger, Dmitry Papush, Nathan Schwartz, Michael Shackleford, Ahmad Shadman, Mike Singer, Louis Spore, Jim Wickwire, and Paul Zotti. We are grateful to Pete Lindquist for suggesting this puzzle.

Acute Dissections

Chris Stembach pointed out a gap in the proof we gave for this puzzle. In regard to the first line drawn, which must end in the interior of the triangle, we stated, "There must be four other lines emanating from the end of [this] first line in order that all of the angles created are acute." We neglected to consider the case where a line passes through the endpoint of the first line. One such line, plus one other line that terminates at the endpoint, could suffice to make all angles acute at the endpoint of the first line. Consideration of this case does not change the final solution. Chris advises, "Actuaries beware. Do not forget to check the validity of your assumptions."