Thread: Finding Sequences Puzzle
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Old 07-27-2010, 11:22 AM   #8
pdurrant
The Grand Mouse 高貴的老鼠
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Quote:
Originally Posted by clarknova View Post
If this is simple then I must be a total moron.

Spoiler:

I need to change my vote, since I picked the first one.

Now I know that 10 THH sequences takes less than 10 THT sequences, but I have no idea why.

On average it takes 80 coin flips to get 10 THH sequences. And it takes 100 flips to get 10 THT sequences (non-overlapping). I really hope someone can explain to me why.

TTT/HHH = 140 flips
THT/HTH = 100 flips
THH/HTT/TTH/HHT = 80 flips

Interestingly, if you use the patterns as binary numbers, and shift left by 1 (multiply by 2), and then multiply by 10 (the number of patterns to detect), you get their average coin flip amounts:

TTT = 111b << 1 = 1110b = 14 (*10 = 140)
THT = 101b << 1 = 1010b = 10 (*10 = 100)
THH = 100b << 1 = 1000b = 8 (*10 = 80)

But I'm still left without the reason. I guess I'll go read the original website.
Lo Zeno has given a good verbal explanation.
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