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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?

Note by Sheikh Asif Imran Shouborno
4 years, 4 months ago

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4 votes

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'h'

As I understand the k's always appear in quantities multiple of 11. Ginaldo Oliveira · 4 years, 4 months ago

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I think it's 'h'. Mursalin Habib · 4 years, 4 months ago

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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 · 4 years, 4 months ago

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@Matthew Lipman Can you please give me a small idea why the digits in the second cycle are 66+121? Vikram Waradpande · 4 years, 4 months ago

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@Vikram Waradpande each of the 11 letters appear exactly 11 more times than in the first cycle. Matthew Lipman · 4 years, 4 months ago

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h Tan Li Xuan · 4 years, 4 months ago

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tttr Bryson Morgan · 1 month, 2 weeks ago

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trwrew Bryson Morgan · 1 month, 2 weeks ago

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tere Bryson Morgan · 1 month, 2 weeks ago

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H , done by geometric sum Calven Tee Chen Kui · 4 years, 4 months ago

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I think L Dishant Shah · 4 years, 4 months ago

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@Dishant Shah There is no 'L'. It goes up to 'k' & starts from 'a' again. Mursalin Habib · 4 years, 4 months ago

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@Mursalin Habib Sorry , i mean A Dishant Shah · 4 years, 4 months ago

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@Dishant Shah How do you say it is "a"?? Sheikh Asif Imran Shouborno · 4 years, 4 months ago

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h?? Superman Son · 4 years, 4 months ago

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