# Why Do We Believe That Catastrophes Come in Threes?

If we stipulate the same year, then the probability falls, of course, but if we allow for birthdays in the same week of the year, the probability rises, and if we consider not 23 but thousands of celebrities of one sort or another, it rises much more. The bottom line is that these celebrity deaths in a relatively short time span are not unusual.

#### Three Puzzles Involving Number Three

Building on this triplebolic mood, I'll end this section by mentioning three puzzles involving the number three. They are among the oddly many such three-puzzles.

One is the Monty Hall 3 door problem, which I discussed in an earlier Who's Counting column.

The second is the 3 hat problem, which I also described in another earlier column.

And the third is the following: Approximately what percent of positive whole numbers contain the digit 3. Some numbers, like 24, 91 and 475, do not contain a 3, but many of them, like 13 and 783, do contain one. The answer is below.

Answer: Almost all whole numbers contain every digit because almost all are more than, say, 1,000 digits long. Any number that long or longer will almost certainly have 3's, 5's, 8's, and every other digit in it.

### Numbers and the Iranian Election

A postscript on the Iranian election: In addition to the resonance many people have for the digit 3, there are affinities and aversions to other digits as well.

In fact, when asked to pick digits randomly, people tend to choose 3 and 7 more often than would occur if the digits were randomly generated.

Moreover, when asked to pick a string of random digits, people tend to choose adjacent digits such as 45 or 89 more often than would occur randomly.

Examining the last digits and the last pairs of digits of the vote totals from various electoral districts in Iran, Bernd Beber and Alexandra Scacco of Columbia University recently concluded that both these tendencies were manifest in the official results.

Since the last digits of the various districts' vote totals would be randomly distributed in a fair election, they inferred that these totals were fabricated by the authorities.

There is some question, however, whether these deviations from randomness are quite as statistically compelling as the authors argue. This, of course, does not mean that the election was not stolen as most threedom-loving people believe.

John Allen Paulos, a professor of mathematics at Temple University, is the author of the best-sellers "Innumeracy" and "A Mathematician Reads the Newspaper," as well as (just out in paperback) "Irreligion: A Mathematician Explains Why The Arguments for God Just Don't Add Up." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.

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