Puzzle #15: Spell It Out
What is the smallest number that contains the letter “a” when spelled out?
There is only one number that, when spelled out, has its letters in alphabetical order. What is it? There is also only one number with its letters in reverse alphabetical order. What is it?
Imagine we fill a dictionary with the first trillion numbers in alphabetical order. What is the first odd number in the dictionary? This question is tougher than it sounds!
Some clarifications:
We’re only considering the counting numbers 1, 2, 3, 4, etc. No fractions, decimals, or negatives.
We’re spelling numbers in a canonical way that does not use the word “and.” For example, the number 426 is written “four hundred twenty six.” The number 2,500 must be written “two thousand five hundred” and cannot be written as “twenty five hundred.” 25,000 on the other hand is written “twenty five thousand.” 100 is written “one hundred” and not “a hundred.”
Ignore all hyphens and spaces. For example, sixteen comes before six thousand.
While some of these might sound like exercises in brute force search, there are strategic ways that you can trim down the search space. Explore the patterns in how we name our numbers and take a stab at whichever prompt you find the most compelling.
Find the solution at the bottom of this page.
