- How many letters does the correct answer to this question contain?
- What is one more than the number of letters in the correct answer to this question?
- What is two more than the number of letters in the correct answer to this question?
- What is the lowest number n for which you cannot answer the question: "What is n more than the number of letters in the correct answer to this question," if you have to give a simple answer (in words)?
- Or, see how far you can go and still come up with an expression to answer that same question for some n.
Find as many answers as you can for each question (also see
here for some interesting ideas).
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Submitted by DJ
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Rating: 4.4167 (12 votes)
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Solution:
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- The only number that is spelled with the number of letters that it denotes is 'four.'
'0' would be another valid answer.
There are many possibilites for longer phrases and sentences which also answer the question, such as:
"7 letters"
"Ten letters"
"42: It's the answer to life, the universe and everything."
Alternatively (although it makes little sense without quotation marks), "the correct answer to this question" contains 30 letters.
- Similarly, there is only one number whose value is one more than the number of letters used to spell it, 'five.'
Also similarly, '1' is a valid answer to the second question.
"8 letters," "fifteen letters," "seventeen letters," etc..
- 'Seven' is the only number with two fewer letters in its spelling than the value it denotes.
Again, '2' is a valid answer to question #3.
Other valid responses include "9 letters," "sixteen letters," "the answer is 12," and many others.
- The fourth question implies that valid answers are of the first form, a number whose value is n more than the number of letters used to spell it. 0, 1, and 2 are listed above; there are two numbers for n=3, six and eight; and four is the lowest n for which no such number exists.
The next lowest n with no such number is 18.
Charlie posted a computer-generated list (and the program in BASIC) up to n=38 here.
- There is no number for which some written expression cannot be found whose value is n more than the number of letters it contains.
Expressions like "plus eleven" or "added to fifteen" (as Brian Smith noted) have a value of one more than the number of letters they contain, so a phrase consisting of "four" followed by n of these expressions will be a new expression for n. For example, "four added to fifteen" works for n=1, "four plus eleven plus eleven" works for n=2, and so on.
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