The 2012th letter

Consider the pattern
abbcccddddeeeee... When the part with 11 "k‘’s end, the pattern continues with 12 "a‘’s, 13 "b‘’s and so on. What is the 2012th letter in this pattern?

Easy Math Editor

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Comments

I think it's 'h'.

Mursalin Habib - 8 years ago

'h'

As I understand the k's always appear in quantities multiple of 11.

Ginaldo Oliveira - 8 years ago

It turns out that the answer is just h.

Proof:

define a "cycle" to be going from an a adjacent to a k to the next k adjacent to an a.

The first cycle has 66 letters. The next has 66+11x11=66+121. The next has 66+2x121. Et cetera

We see that the first five cycles have 66x5+121x10=1540 letters. This leaves 472 letters. We see that in the sixth cycle, a occurs 56 times.

This leaves 416 letters after the a's.

This leaves 416-57=359 letters after the b's.

This leaves 359-58=301 letters after the c's.

This leaves 301-59=242 letters after the d's.

182 after e's, 121 after f's, 59 after g's

H.

Matthew Lipman - 8 years ago

Can you please give me a small idea why the digits in the second cycle are 66+121?

Vikram Waradpande - 8 years ago

each of the 11 letters appear exactly 11 more times than in the first cycle.

Matthew Lipman - 8 years ago

h

Tan Li Xuan - 8 years ago

tere

bryson morgan - 3 years, 10 months ago

trwrew

bryson morgan - 3 years, 10 months ago

tttr

bryson morgan - 3 years, 10 months ago

H , done by geometric sum

Calven Tee Chen Kui - 8 years ago

h??

superman son - 8 years ago

I think L

Dishant Shah - 8 years ago

There is no 'L'. It goes up to 'k' & starts from 'a' again.

Mursalin Habib - 8 years ago

Sorry , i mean A

Dishant Shah - 8 years ago

@Dishant Shah – How do you say it is "a"??

Sheikh Asif Imran Shouborno - 8 years ago