Suppose that each number from 1 to 10,000,000,000 written in English and then alphabetically arranged (as in a dictionary) while ignoring spaces and hyphens. What would be the first odd number in the list?

## Solution

This kind of problem should be solved step by step. You have to take into account the successive words that described the number. First, determine the digit that would appear first in a dictionary. Upon some thought, you can easily figure out that it’s “eight”. Now, think of the next earliest available word that follows “eight”. The earliest word is “billion”. So, the answer is eight billion something…

Following the same logic, you can determine the answer: 8,018,018,885 (eight billion eighteen million eighteen thousand eight hundred eighty-five ).

This odd problem is based on the problem posted by computer scientist Donald Knuth. His problem was: “What is the first prime number in the dictionary?” The way to solve this puzzle is similar to the method outlined above. After some checking on a computer, you would eventually get the answer: 8,018,018,851.

Hi… err… How BIG is this Dictionary.?.

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Knuth”s stuff is fun… had forgotten about him for years. But I am wondering something. Why wouldn’t the verbal representation of the number 8,000,000,008 precede the answer you have given in alphabetical order? It seems it would either be represented as ‘eight billion eight’ or perhaps ‘eight billion and eight’. Either way this seems to come earlier in sequence than the answer you’ve given.

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His books were indeed fun back in the days.

To answer your question, it’s because it’s not an odd number.

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ah, got it. 🙂

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No, but 8,000,000,001 is odd. In England we say “Eight billion and one”.

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Ouch… brain ache!!

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Great puzzle, with a unique and clever answer!

I think rather than “Suppose that each number from 1 to 10,000,000 written in English” it should be 1 to 10,000,000,000.

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Thanks for informing me about the typo. At first I wrote it as 10^10 but I wanted to make it clearer so I wrote the number. Too bad, I made it more confusing lol.

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Sorry, I’m being a bit of a nitpicker today but I think the first prime in the dictionary listed as “8,018,018,881” is actually composite as it’s divisible by 37.

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It must be my bad day yesterday…

The answer should be 8,018,018,851.

Thanks again.

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｢(ﾟ<ﾟ)ﾞ??

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