What is the only number...?

Question

The "letter level" of a number denotes how many letters it contains when written out. Hyphens and spaces do not count. What is the only number between 1 and 5,000 such that it is the only member of its letter level. (Also, you say one hundred, not a hundred)

Answer 1

I'll try to do it somewhat systematically ...
3 one; two
5 three; seven
4 four; five
6 eleven; twelve
8 thirteen; fourteen
7 fifteen; sixteen
9 seventeen; twenty one
11 twenty three; twenty seven
10 twenty four; twenty five
12 seventy three; seventy seven
13 one hundred one; one hundred two
14 one hundred four; one hundred five
15 one hundred seven; one hundred eight
16 four hundred seven; four hundred eight
17 seven hundred seven; seven hundred eight

I see some patterns here ... let's jump to the largest letter level between 1 and 5000 ...

37 three thousand three hundred seventy three

So the answer has a letter level somewhere between 18 and 36. Let's continue ...

18 seven hundred eleven; seven hundred twelve
19 seven hundred fifteen; seven hundred sixteen
20 seven hundred thirteen; seven hundred fourteen
21 seven hundred seventeen; seven hundred twenty one
22 seven hundred twenty four; seven hundred twenty five
23 seven hundred twenty three; seven hundred twenty seven
24 seven hundred seventy three; seven hundred seventy seven

Hmmm ... we have to go over one thousand.

25 one thousand one hundred four; 1105
26 one thousand one hundred three; 1107
27 one thousand four hundred three; 1407
28 one thousand three hundred three; 1307
29 four thousand three hundred three; 4307
30 three thousand three hundred three; 3307
31 three thousand three hundred eleven; 3312
32 three thousand three hundred fifteen; 3316
33 three thousand three hundred thirteen; 3314
34 three thousand three hundred seventeen; 3321
35 three thousand three hundred twenty four; 3325
36 three thousand three hundred twenty three; 3327
37 three thousand three hundred seventy three; 3377

There's nothing bigger. So something is wrong; there's no number between 1 and 5000 that has a unique number level. This exercise seems like a waste of time.

Answer 2

3000

Answer 3

4

Four has four letters, so this certainly satisfies your criteria. This isn't a proof that it is the only one between 1 and 5,000 that fits though!

Answer 4

three thousand eight hundred eighty eight

Answer 5

dghj

Answer 6

4 (four)...i tink..

Answer 7

un.