A Muppet You Can Count On

A big MJ4MF thanks to Lindsey Witcosky, who directed me to a wonderful BBC article about one of my favorite Sesame Street characters, the Count! The link to the article is provided below, but first a quiz based on some trivia in the article.

1. What was the Count’s full name?

2. What was the Count’s favorite number?

3. Who was the voice of the Count from 1970 until 2011?

Answers are below, but you can also find them in the BBC article:
http://www.bbc.co.uk/news/magazine-19409960

The Count’s favorite number is equal to 187², and BBC Radio asked listeners of the show More or Less to speculate why. One listener noted that 187 = 94² ‑ 93² and, of course, 187 = 94 + 93. The BBC article referred to this coincidence as, “An embarrassment of riches!” But I prefer to think of it as, “An embarassment of algebra!”

Algebra can be used to show why this is true. The nth square number is equal to the sum of the first n positive odd integers. That is,

n² = 1 + 3 + 5 + 7 + … + (2n ‑ 1)

From this it follows that

94² = 1 + 3 + 5 + 7 + … + (2 × 94 – 1)

and

93² = 1 + 3 + 5 + 7 + … + (2 × 93 – 1)

so of course

94² – 93² = 2 × 94 – 1 = 187

Moreover, the difference of two squares is equal to the product of the sum and difference of the two numbers. That is,

a² ‑ b² = (a + b)(a ‑ b)

Consequently,

187 = 94² ‑ 93² = (94 + 93)(94 ‑ 93) = (94 + 93)(1)

So, saying that 187 = 94² ‑ 93² = 94 + 93 is kind of like saying the same thing twice, just in different ways.

Answers

1. Count von Count

2. 34,969

3. Jerry Nelson, who passed away on August 23. R. I. P.

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