*This was a puzzler that I'm stealing from the late Martin Gardner. I'm going to give you a number and you're going to tell me what's unique about the following number: 8,549,176,320. Now if you want a hint, I'll point out that there are 10 digits in that number. The question is, what's unique about this number?*

The answer requires some linguistic gymnastics. The extra puzzles are somewhat hidden until the first puzzle is solved:

The number 8,549,176,320 is the result of taking the written form of each numeral and alphabetizing them from A-Z.

So this list

**Z**ero

**O**ne

**T**wo

**T**hree

**F**our

**F**ive

**S**ix

**S**even

**E**ight

**N**ineBecomes this number

**E**ight

**F**ive

**F**our

**N**ine

**O**ne

**S**even

**S**ix

**T**hree

**T**wo

**Z**eroor 8,549,176,320 (note that one could argue that 236,719,458 is every bit as "unique" in this same sense).

While gnawing on this otherwise trivial puzzle, I noticed a couple of more interesting facts.

- There are three letters that start two numbers:
**T**()**t**wo,**t**hree**F**(**f**our,**f**ive**S**(). In all three cases, the numbers are consecutive, hence the letters "pattern together" in a certain sense (also notice that in the alphabetized version, each pair's order is reversed). Is there any historical reason for this, or just coincidence? Care to write a FOPC statement that correctly captures this fact?**s**ix,**s**even

- It became quite clear to me that accessing numbers and lexical items interfere with each other while trying to write the number down. Since I was driving in a car when I first heard the puzzler, I didn't write the number down, but I figured I could reconstruct it easily, but then I jumped on the DC metro with no writing tool, so I couldn't write down the letters then alphabetize them in front of my eyes, so I had to "figure it out" in my head. No worries, I thought, I'm a smart guy and a little Saturday morning brain tease is better than coffee. So I flipped out my archaic, obsolete cell phone and wrote the number into a text message. What I discovered was something akin to a numerical Stroop effect where the numbers interfered with my ability to choose the correct button to push. So I wanted to type the letter "T" for "two" (which is the number 8 on my keypad), but instead I typed the letter "A" because that's on the number 2 button. I had a similar problem just now when typing on a full keyboard. When I tried typing the number names above, I regularly typed the number from the topmost key row instead. Somebody must have studied this kind of interference already, right?

## 2 comments:

The numeral-pairing has been mentioned and I know there has been some literature on it (maybe something cited in Hurford's _Language and Number_?). It's pretty widespread in the Indo-European languages of Europe (e.g. duo/tres, quattuor/quinque, sex/septem) but sporadic elsewhere. On the other hand, it appears in other languages - e.g. Japanese, but not in successive numerals: http://paleoglot.blogspot.com/2008/02/hidden-binary-behind-japanese-numeral.html .

There are many different numerical Stroop effects, some of which are talked about by Stanislas Dehaene in his _The Number Sense_, others known mostly in the specialist literature on numerical cognition. I can't recall where I first heard of the one you mention but I've certainly experienced it. I'm doing some work on phone numbers right now so this is a particular interest of mine.

- Steve Chrisomalis

Steve, thanks for the excellent link and suggestions! I knew there had to be something out there.

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