Answer to July 2004 Newsletter Brain Teaser:

There is a 20% chance.

First, there are a total of 90 room-number combinations that work. The first number can only be 1, 2 or 3. The last number can only be 4, 5, or 6. The middle number can be 0-9 (or any of 10 numbers).

For example, 104, 105, 106 all work, and then 114, 115, and 116... and so on. This works out to be 30 (10 * 3) for each first digit, or at total of 30 + 30 + 30 = 90. 90 possibilities...out of 450 rooms.

This is a 90/450 or a 20% probability.