One-Dollar Words Problems

Here are some problems that relate to one dollar words; see the one dollar words page for more information about what these are.

Some of these problems can be challenging.

1. Out of all numbers less than one thousand, which one has the highest dollar word value?
2. There are two numbers less than 100 that have a dollar value of $1. What are they?
3. If a certain number of dollars and cents is written as words, and its dollar word value calculated, the result is the same as the original number. What is the number?
4. There are no numbers which, if written out as English words, have a dollar word value (in cents) equal to their value. However, if the word "and" were to be included after the word "hundreds" (e.g. writing 105 as "one hundred and five"), there are two such numbers. Can you find both? Hint: They are fairly close together.
5. There are five different numbers less than one hundred that all have the same dollar word value. What are the numbers?

Answers can be found on the answers page.

Further investigation: If you like one-dollar words, here are some ideas for further investigation.

• Read the page on loops and looping. What happens when you loop one dollar words? As an example, "thirty" has a one dollar word value of $1.00. Taking $1.00 as "one hundred", that has a one dollar word value of $1.08. "One hundred and eight" has a dollar word value of $1.57. Do the numbers keep increasing? Settle at a single number? Reach a loop?
• I'm aware of 966 one-dollar words. How many words are there with a different dollar value, say, 67¢, or $1.08? For which value are there the most words?
• If you know any foreign languages, look for one-dollar words in those languages, and try answering some of the above questions in that language.
• What if you changed the rules in some manner? For example,What if you changed the values for each letter in some manner, or what if you multiplied the values together instead of adding, or added and subtracted alternate letter values? Pick something to change and see what happens.

Some thoughts about some of these can be found on the answers page.

You can find some other ideas for exploration on pages 114–116 of Beyond Language by Dmitri Borgmann.