### Solution to June's Puzzle: Same Birthday

What's the probability that, in a group of 23 randomly chosen people, at least two of them will have the same birthday? The answer to this puzzle might seem strange. Most people intuitively assume that the probability is very low. However, the probability that two people in a group of 23 have the same birthday happens to be greater than 50 percent (about 50.7 percent). For 60 or more people, it's greater than 99 percent (disregarding variations in the distribution, and assuming that the 365 possible birthdays are equally likely). The tricky part of the puzzle is that you need to determine the probability that *any* two people share the same birthday—not a *specific* two. For the exact solution and some interesting information about the birthday paradox, check out the Wikipedia entry at http://en.wikipedia.org/wiki/birthday_paradox

### July's Puzzle: Catching a Train

Two trains race toward each other on a railway segment that's 100 miles long. The trains are traveling at 100mph. An insect flying at 200mph flits from one train toward the other, and as soon as it arrives at the other, it flips its direction and flies back toward the first train. The insect continues bouncing back and forth between the trains until the trains crash. What's the total distance that the insect covers until the moment of the crash?