New Scientist Enigma Puzzle 1763 - Number Theory

Main post link -> http://www.newscientist.com/article/mg21929310.600-enigma-number-1763.html#.UhvP7qO3PFo

http://www.newscientist.com/article/mg21929310.600-enigma-number-1763.html#.UhvP7qO3PFo

The problem basically seeks a number with a unique number of letters when written out in English from a given set (even and divides 3 or odd and divides 3)

Okay, so I solved this using python, by finding the frequency distribution of the number of letters in a written figure. Then finding which figures contained, say, 10 letters when written in full.

I was trying to figure out how to do this with just a pen and paper. Any observations would be much appreciated. Specifically, how can I prove/ When can I assume that the word length frequency follows an approximate bell curve?

My Inelegant but functional Python code available if anyone wants to see.

#NumberTheory #ComputerScience #CoolLinks #HelpMe! #Advice #MathProblem #Math

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

Is it over or did you submit the answer?

Justin Wong - 7 years, 9 months ago

I already have the answer and I'll submit when I get round to it.

I was just a little unsatisfied with my method and wondered how to solve it by hand.

Jamie Coombes - 7 years, 9 months ago

Just submitted the answer to enigma@newscientist.com. Any thoughts?

Jamie Coombes - 7 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$