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?

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?

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## Comments

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TopNewest'h'

As I understand the k's always appear in quantities multiple of 11. – Ginaldo Oliveira · 3 years, 8 months ago

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I think it's 'h'. – Mursalin Habib · 3 years, 8 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 · 3 years, 8 months ago

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– Vikram Waradpande · 3 years, 8 months ago

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

– Matthew Lipman · 3 years, 8 months ago

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

h – Tan Li Xuan · 3 years, 8 months ago

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H , done by geometric sum – Calven Tee Chen Kui · 3 years, 8 months ago

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I think L – Dishant Shah · 3 years, 8 months ago

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– Mursalin Habib · 3 years, 8 months ago

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

– Dishant Shah · 3 years, 8 months ago

Sorry , i mean ALog in to reply

– Sheikh Asif Imran Shouborno · 3 years, 8 months ago

How do you say it is "a"??Log in to reply

h?? – Superman Son · 3 years, 8 months ago

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