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 Counting Exercise (Posted on 2003-09-10)
1. How many letters does the correct answer to this question contain?

2. What is one more than the number of letters in the correct answer to this question?

3. What is two more than the number of letters in the correct answer to this question?

4. 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)?

5. 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).

 See The Solution Submitted by DJ Rating: 4.4167 (12 votes)

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 solution | Comment 4 of 9 |
Question 1 has several interpretations, so the answers fall into different categories:

1. 0
This answer indeed has zero letters--only a digit.

2. Four.
This answer indeed has four letters.

The totality of this answer, as a sentence indeed has 11 letters.

4. Wording similar to option 3, but somewhat different, with various numbers being correct depending on how many letters there are in the verbiage, such as "The answer has 19 letters."

5. The answer has twenty-nine letters.
This is also extensible with various wordings, and it ties into the subsequent questions on the list, as here we needed a number name that had a value 19 more than the number of letters in that number name. Again, variations are such as "The answer is nineteen."

Question 2 again has variations.

1. 1

2. Five.

4. Variations in wording on 3.

5. The answer is twenty-one, and its variations in verbiage.

Question 3 has the usual variations as above, including the one that is unique to it: "seven".

In answering question 4, let's first consider this straightforward single-word-number-oriented intepretation (four, five, seven, ...). There is no similar answer like this for n=4. That's because there are two answers for n=3 ("six" and "eight") and three such answers for n=5 ("nine", "eleven" and "thirteen"). While n can increase in general with the numbers, there are some that are repeated while others do not appear, and the first of these is n=4.

Of course nothing precludes something like "That's 9." or "It's ten." as answers for n=4, and similar verbiages that can be used as work-arounds for any value of n.

Of use in coming up with such answers is a table, ordered by the difference between the signification and the length, of the number words. The following table shows that difference, the signified number, the length of the number name and the name itself:
```
0   4   4 four

1   5   4 five

2   7   5 seven

3   6   3 six

3   8   5 eight

5   9   4 nine

5  11   6 eleven

5  13   8 thirteen

6  12   6 twelve

6  14   8 fourteen

7  10   3 ten

8  15   7 fifteen

8  17   9 seventeen

9  16   7 sixteen

10  18   8 eighteen

11  19   8 nineteen

12  21   9 twenty-one

12  23  11 twenty-three

13  22   9 twenty-two

14  20   6 twenty

14  24  10 twenty-four

15  25  10 twenty-five

16  27  11 twenty-seven

17  26   9 twenty-six

17  28  11 twenty-eight

19  29  10 twenty-nine

22  31   9 thirty-one

22  33  11 thirty-three

23  32   9 thirty-two

24  30   6 thirty

24  34  10 thirty-four

25  35  10 thirty-five

26  37  11 thirty-seven

27  36   9 thirty-six

27  38  11 thirty-eight

29  39  10 thirty-nine

33  41   8 forty-one

33  43  10 forty-three

34  42   8 forty-two

35  40   5 forty

35  44   9 forty-four

36  45   9 forty-five

37  47  10 forty-seven

38  46   8 forty-six

38  48  10 forty-eight

```

--------
This table was produced by a computer program whose output was then sorted by the first column. Three negative values were discarded (-1 for "two" and -2 for "one" and "three").

DECLARE SUB ProcPiece (piece\$, MajorPower!)
DATA one,two,three,four,five,six,seven,eight,nine
DATA ten,eleven,twelve,thirteen,fourteen,fifteen,sixteen,seventeen
DATA eighteen,nineteen
DATA twenty,thirty,forty,fifty,sixty,seventy,eighty,ninety
DIM SHARED unit\$(19), ten\$(10), major\$(7)
FOR i = 1 TO 19
NEXT
FOR i = 2 TO 9
NEXT
FOR i = 1 TO 7
NEXT
DIM SHARED name\$, num\$
OPEN "reptqest.txt" FOR OUTPUT AS #1
FOR n = 1 TO 100
num\$ = LTRIM\$(STR\$(n))
IF num\$ = "0" THEN
name\$ = "zero"
ELSE
name\$ = ""
MajorPower = 0
DO
l = LEN(num\$): IF l > 3 THEN l = 3
piece\$ = RIGHT\$(num\$, l)
num\$ = LEFT\$(num\$, LEN(num\$) - l)
CALL ProcPiece(piece\$, MajorPower)
MajorPower = MajorPower + 1
LOOP WHILE LEN(num\$) > 0
END IF
numLets = 0
FOR i = 1 TO LEN(name\$)
IF INSTR("abcdefghijklmnopqrstuvwxyz", LCASE\$(MID\$(name\$, i, 1))) > 0 THEN
numLets = numLets + 1
END IF
NEXT
PRINT #1, USING "### ### ### &"; n - numLets; n; numLets; name\$
NEXT
CLOSE

SUB ProcPiece (piece\$, MajorPower)
piece = VAL(piece\$)
n\$ = ""
IF piece > 99 THEN
n\$ = unit\$(piece \ 100) + " hundred "
piece = piece MOD 100
END IF
IF piece > 19 THEN
n\$ = n\$ + ten\$(piece \ 10)
piece = piece MOD 10
IF piece > 0 THEN n\$ = n\$ + "-": ELSE n\$ = n\$ + " "
END IF
IF piece > 0 THEN n\$ = n\$ + unit\$(piece) + " "
IF n\$ > "" THEN name\$ = n\$ + major\$(MajorPower) + " " + name\$
END SUB

 Posted by Charlie on 2003-09-10 16:04:20

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