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Finding Sequences Puzzle
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07-27-2010, 11:22 AM
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pdurrant
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Quote:
Originally Posted by
clarknova
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.
pdurrant
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