Flip the Alphabet
August 3, 2015 8:30 AM Subscribe
26 spaces across. You start with
AAAAAAAAAAAAAAAAAAAAAAAAAA and follow with
AAAAAAAAAAAAAAAAAAAAAAAAAB;
AAAAAAAAAAAAAAAAAAAAAAAABB;
AAAAAAAAAAAAAAAAAAAAAAABBB; proceeding to
...
BBBBBBBBBBBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBBBBBBBBBBBBC, etc. until
...
YZZZZZZZZZZZZZZZZZZZZZZZZZ; finally ending with
ZZZZZZZZZZZZZZZZZZZZZZZZZZ.
How many lines would you have after you did this for the whole alphabet?
Best answer: 651 I think. Each letter has 26 copies of itself which could end the sequence, except for A which only has one copy. So 26*26-25=651.
posted by noneuclidean at 8:37 AM on August 3, 2015
posted by noneuclidean at 8:37 AM on August 3, 2015
Best answer: Yes, noneuclidean has it right. You can think of your sequence as windows over a long string of letters:
AAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCCCC.....
The whole string of letters is 676 characters long (26*26). You are choosing a window size of 26 and you always want it filled, so you need to subtract 25 from the length of the string to get the total number of valid positions, giving you 651.
posted by demiurge at 9:03 AM on August 3, 2015 [3 favorites]
AAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCCCC.....
The whole string of letters is 676 characters long (26*26). You are choosing a window size of 26 and you always want it filled, so you need to subtract 25 from the length of the string to get the total number of valid positions, giving you 651.
posted by demiurge at 9:03 AM on August 3, 2015 [3 favorites]
You have 26 character spaces. Each space has 26 possible characters. So that's 26^26.
To understand why, try it with numbers: 10 spaces, possible digits 0-9. First line is 0000000000, last line is 9999999999. You'll see that 10^10 is 10000000000, which is one number higher than the last line, because the first line is all zeroes.
posted by trivia genius at 9:03 AM on August 3, 2015
To understand why, try it with numbers: 10 spaces, possible digits 0-9. First line is 0000000000, last line is 9999999999. You'll see that 10^10 is 10000000000, which is one number higher than the last line, because the first line is all zeroes.
posted by trivia genius at 9:03 AM on August 3, 2015
Oops, After seeing demiurge's answer, I think I misunderstood your question. Yes, 651 is right for your question.
posted by trivia genius at 9:04 AM on August 3, 2015
posted by trivia genius at 9:04 AM on August 3, 2015
Response by poster: Thanks!
FYI, I have decided to add 25 lines to the beginning-- for
A
AA
AAA...
etc.
and 25 lines to the end-- for
...
ZZZ
ZZ
Z,
making it 701.
posted by cake vandal at 9:21 AM on August 3, 2015
FYI, I have decided to add 25 lines to the beginning-- for
A
AA
AAA...
etc.
and 25 lines to the end-- for
...
ZZZ
ZZ
Z,
making it 701.
posted by cake vandal at 9:21 AM on August 3, 2015
This thread is closed to new comments.
posted by JoeZydeco at 8:34 AM on August 3, 2015 [1 favorite]