## Posts tagged ‘repeated’

### Happy 100/9 Day

Today is a special day indeed. You may have already noticed that today’s date is the repetitive 11/11/11, but did you know that **today is the only date this century that can be written in the form mm/dd/yy with one digit repeated six times**?

Some people celebrate 3/14 as Pi Day, and to ensure complete precision for their celebration, the moment at which they celebrate is 1:59:26 p.m. In a similar vein, I suggest that we all celebrate “100/9 Day” at 11:11.11 a.m. today. Too bad 100/9 doesn’t have a Greek letter nickname for which it is better known…

Not too long ago, I was forwarded an email that contained several pieces of numerical trivia. The first was this:

This year we’re going to experience four unusual dates: 1/1/11, 1/11/11, 11/1/11, and 11/11/11.

Today is one of those dates, and it is certainly unusual for a date to contain only one repeated digit. The only other dates with just one repeated digit during this century are 2/2/22, 2/22/22, 3/3/33, 4/4/44, 5/5/55, 6/6/66, 7/7/77, 8/8/88 and 9/9/99. Since there are only 13 dates that contain just one repeated digit, it could also be said that 2011 is an unusual year for hosting four of them.

The email also contained the following:

Take the last two digits of the year in which you were born. Now add the age you will be this year. The result will be 111 for everyone in the whole world.

Blanket mathematical statements like this one are frustrating, especially when they are untrue. My friend’s grandfather was born in 1899, so he will turn 112 this year. For him, the result is 99 + 112 = 211. And my sons were born in 2007 and turned 4 this year. For them, the result is 7 + 4 = 11. In fact, based on data about age distribution, the result will **not** be 111 for approximately 15% of the U.S. population. The yellow bars in the graph below indicate the ages for which this trick does not work.

A better statement of this “trick” might be…

Take the year in which you were born. Now add the age that you will be this year. The result will be 2011 for everyone in the whole, wide world.

Wow! Can you believe it? But it’s not much of a trick anymore, is it?

Happy 100/9 Day, everybody!

**[Update]** This post originally appeared as “Happy 10/9 Day,” but that was in error. I blame sleep deprivation. It has been updated to “100/9 Day” in all places.

### Coming Up Through the Ranks

Through some special features at Amazon Author Central, I am able to know the daily sales rank of Math Jokes 4 Mathy Folks. My sales rank at the end of each of the last three days was 44,404, 96,990, and 35,355, respectively. I thought that was interesting — three days in a row when the sales rank was a five-digit number in which one digit occurred at least three times. What’s the likelihood of that? Stated more formally:

Assuming that the sales rank of MJ4MF is always a five-digit number, what is the probability that three consecutive days’ sales ranks will contain a digit that occurs in the sales rank at least three times?

The sales rank of MJ4MF has never been a five-digit number in which the same digit is repeated five times. (Bummer!) The probability of that occurrence, though, is even less likely than the situation described above — though I won’t tell you exactly how much less likely, so as not to spoil your fun!