Wes Carroll's Puzzler

A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers choose their spaces at random from among the available spaces. Santa Claus then arrives in his oversized and very full sleigh, which requires two adjacent spaces. What is the probability that there’s a place for him? // Spiciness: **** out of ****

What’s the largest 2-digit prime factor of “200 choose 100”? // Spiciness: *** out of ****

Last week, two of my friends and I went to a restaurant and had a lovely meal. We decided to evenly split the check, so we asked the waiter to just combine the totals. However, when the waiter came with the check, he revealed that there had been a mistake and instead of recording the complete total, the computer only returned a list of the totals of each pair of people. // Spiciness: * out of ****

A faulty car odometer proceeds from digit 3 to digit 5, always skipping the digit 4, regardless of position. For example, after traveling one mile the odometer changed from 000039 to 000050. If the odometer now reads 001729, how many miles has the car actually traveled? // Spiciness: *** out of ****

How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits? // Spiciness: ** out of ****