Mathematical Entertainments Michael Kleber and Ravi Vakil, Editors
drove away and I was unable to follow. I’ll never know if Mathematical he was aware that the state had assigned one of the most important numbers in mathematics to his car. How I envied Vanity Plates him! Indeed, 65536 is not just an ordinary power of 2, and not simply the order of the multiplicative group in the Galois field of the largest known Fermat prime. It is DONALD E. KNUTH 20 22 22 22 ¼ 22 ; a number of huge importance in computer algorithms. This column is a place for those bits of contagious Already in 1967 I had become a big fan of this number, and my appreciation has continued to grow as I continue to mathematics that travel from person to person in the learn more.
community, because they are so elegant, surprising, or The Old Rules appealing that one has an urge to pass them on. In those days each state of the USA required its drivers to purchase new license plates with new license numbers Contributions are most welcome. every few years, assigning the values in sequence. Thus your chance of getting any particular number n was at most 1/n. People began to covet the small numbers—not because Extracted from the author’s book Selected Papers on Fun small numbers are mathematically interesting (which they and Games (2010) CSLI Publications, Stanford. are), but because small numbers are easy to remember. Small numbers also connote rank: The governor was num- ber 1. The New York Times reported in 1959 [39] that his story began in the spring of 1967 when I made a Low-numbered ‘‘vanity’’ plates have had a long and dis- visit to Madison, Wisconsin, in order to give a tinguished history in the automobile business. They have TT lecture at the university. I was driving near the traditionally been obtained by politicians for their friends campus on a fine, sunny day. There was moderate traffic, and campaign contributors. They have long been dog- and when a red light stopped me I happened to glance at gedly sought after by celebrities, egomaniacs and men the license plate of the car ahead. My jaw dropped—wow! who have everything. Last year about 69,000 New York- It said ‘‘H65 536’’. I can still picture that plate in my mind, ers paid $5 extra for special low-numbered plates. as plain as day, although more than forty years have About 5 million automobiles were registered in New York passed; in fact, with modern software, I now can recreate state at that time; New York plates contained one or two its exact appearance: letters to encode a county, together with a serial number. Clever people didn’t actually have to settle for a random number on their licenses, however. It was perfectly legal in many states, including New York and California, to get your plates in a remote county, far from where you lived. During a vacation to a sparsely populated area, you could drop in to the local office and obtain decent numbers without I started to jump out of my car, thinking that I might much competition. Furthermore, your initials might well be approach the driver to ask him if he knew what a fantastic available in some rural county. license number he owned. But the light turned green; he My father-in-law, who lived at 525 Summit Street in the medium-sized city of Fostoria, Ohio, was able to drive Ohio 525 S â plates reading (his address) ever since the 1950s, Please send all submissions to the Mathematical because he was a friend of the local people who were in Entertainments Editor, Ravi Vakil, Stanford University, charge of auto registration. Department of Mathematics, Bldg. 380, Stanford, Beginning in 1967, Wisconsin motorists could obtain CA 94305-2125, USA plates of the forms A9, A99, A999, A9999,orAA999 by e-mail: [email protected] paying a surcharge, where A denotes any letter and 9