cockbeard wrote:Right I think I might get youSpoiler:
GooberTheHat wrote:Is it correct to assume that the bridge contracts at the same rate once the caterpillar has crossed the halfway point?
The Daddy wrote:This is a bit like the Achilles and the tortoise puzzle isn't it? I use that when I introduce mechanics at A level. The caterpillar guy moves with the stretch, so at the beginning of day 2 he's still 1% across the bridge even though it's lengthened. And so on.
acemuzzy wrote:Wrong! As above, the proportion of the bridge he's covered is 1/100 x (1+1/2+1/3+1/4+...) = 1/100 x (1 + 1/2 + (1/3+1/4) + (1/5+1/6+1/7+1/8 ) + (1/9+...1/16) + ...) > 1/100 x (1 + 1/2 + 1/2 + 1/2 + 1/2 + ...) So he will definitely make it. It's just the nth half-percent of progress takes him order 2^n moves, and yeah 2^200 is like fucking enormous... Very counter-intuitive though, I still can't quite get my head round it. I have another question about maths by the way. And one about dice...
So you inferred it was the sum of a series not from the puzzle but from someone writing out a series with plus signs in? GeniusSpaceGazelle wrote:I haven't even bothered to look at the puzzle but isn't it just the sum of a series?
cockbeard wrote:1 606 938 044 258 990 275 541 962 092 341 162 602 522 202 993 782 792 835 301 376 It's a lot, 1.6 Novemdecillion, yes of course I looked that word up
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