Why is Sesame Street's Count von Count's favorite number $34,\!969$? [closed]

In the 2 minute BBC News audio clip Sesame Street: What is Count von Count's favourite number? "The Count" is asked

Do you have a favorite number?

to which he replied

Thirty four thousand, nine hundred and sixty nine. It's a square root thing.

Does the number 34,969 have any particularly notable properties that would make it "The Count"'s favorite number?

Revelations from the world of counting from the late Jerry Nelson, the voice of Count von Count, who was interviewed by Tim Harford to mark Sesame Street's 40th anniversary in 2009.

Photo: Count von Count attends Macy's Thanksgiving Parade 2018 Credit: Getty Images

Release date: 01 February 2019 Duration: 2 minutes

• Well, $34969 = 187^2$. Commented Feb 2, 2019 at 22:11
• To go the other way $34969 = \sqrt{1222830961}$. I think we just have to accept that this was just a dry joke. Given infinite numbers it's funny if one's favorite number is something arbitrary. And it's funnier if one gives a reason that, although not incorrect, reveals little. Commented Feb 2, 2019 at 22:27
• "Does the number 34,969 have any particularly notable properties that would make it "The Count"'s favorite number?" Yes! Commented Feb 2, 2019 at 23:49
• Why does this have so many upvotes?? Commented Feb 3, 2019 at 5:03
• @YiFan: This community seems to have a fondness for bat-related things.
– Blue
Commented Feb 3, 2019 at 6:59

There are some speculations in the following article:

https://www.bbc.com/news/magazine-19409960

The following is taken verbatim from the link:

34,969 is 187 squared. But why 187?

More or Less turned to its listeners for help.

Toby Lewis noted that 187 is the total number of points on the tiles of a Scrabble game, speculating that the Count might have counted them.

David Lees noticed that 187 is the product of two primes - 11 and 17 - which makes 34,969 a very fine number indeed, being 11 squared times 17 squared. What, he asked, could be lovelier?

And Simon Philips calculated that 187 is 94 squared minus 93 squared - and of course 187 is also 94 plus 93 (although that would be true of any two consecutive numbers, as reader Lynn Wragg pointed out). An embarrassment of riches!

But both he and Toby Lewis hinted at darkness behind the Count's carefree laughter and charming flashes of lightning: 187 is also the American police code for murder.

Murder squared: was the Count trying to tell us something?

• 0d187 = 0d11 * 0x11. Is that interesting? Commented Feb 3, 2019 at 1:11
• The difference of squares observation is interesting given that the prime factorization indicates $187 = 11 \cdot 17 = (14-3)(14+3) = 14^2 - 3^2$. Commented Feb 3, 2019 at 17:11
• It's very hard to choose an answer to accept, but in this particular case I'm going to go with the quoted source. Thanks everyone!
– uhoh
Commented Feb 4, 2019 at 9:00

Curiously, $$\sqrt{1234567890}=35136.418\ldots$$ which is kinda-sorta close to $$34969$$, although it doesn't seem close enough to make the joke work.

Perhaps it's that $$34969=187^2$$ is the largest perfect square whose own square doesn't exceed $$1234567890$$ (since $$\sqrt[4]{1234567890} = 187.447\ldots$$).

Considering how the Count counts, one might think his favorite number relates to $$12345678910$$ It's perhaps worth noting that \begin{align} \sqrt{12345678910} &\;=\; 111,111.11\ldots \\ \sqrt[4]{12345678910} &\;=\; \phantom{111,}333.33333\ldots \end{align} where I have conveniently truncated the digits for best effect.

Unrelatedly: I've always been a little disappointed that the Count's full name is "Count von Count" instead of, say, "Count von Tuthrifore".

• That definitely ought to be his name! Commented Feb 3, 2019 at 2:21
• @timtfj: And then his daughter Zira could grow up to be a combinatorist and/or a programmer. :)
– Blue
Commented Feb 3, 2019 at 3:02

Presumably if it's a square root thing, we're allowed to consider its square root, which, as other answers have noted, is $$187$$.

According to David Wells, The Penguin Dictionary of Curious and Interesting Numbers, (Penguin, 1986), $$187$$ is

The smallest of a group of $$3$$-digit numbers that require $$23$$ reversals to form a palindrome.

This is then followed by the entry for $$196$$, which includes an explanation of palindromes by reversal. The procedure is to reverse a number's digits and add the resulting number to the original.

Do all numbers become palindromes eventually? The answer to this problem is not known. $$196$$ is the only number less than $$10,000$$ that by this process has not yet produced a palindrome. P. C. Leyland has performed $$50,000$$ reversals, producing a number of more than $$26,000$$ digits with no palindrome appearing, and P. Anderton has taken this up to $$70,928$$ digits, also without success.

Most of the $$3$$-digit numbers require only a few reversals. The ones needing $$23$$ are

$$\{187, 286, 385, 583, 682, 781, 880\},$$

all of which go via $$968$$ then $$1837$$, and end up at $$8813200023188$$.

So my guess is that the Count is able to take the square root of $$34969$$ in his head then do the $$23$$ reversals and get the palindrome, but hasn't yet managed to do the same with $$38416=196^2$$.

• $968$ presumably only needs $22$ because it is the result of most of the others. Commented Feb 3, 2019 at 1:57
• @RossMillikan That must be right. I'll reword it a bit. Commented Feb 3, 2019 at 2:01
• @RossMillikan And it must apply to $869$ as well. Commented Feb 3, 2019 at 2:04