If I want to make a Damascus blade with 1000 layers, how many layers do I need to start with so that I end up with 1000 layers? What equation can I use to get the right answer? Please show each step when answering.

gibsonj338 Sep 21, 2018

#1**+1 **

125 ? Not sure how to make a damascus blade....but if you fold it in half several times to complete it, the whole number 125 will work

125 fold in half = 250 fold in half = 500 fold in half = 1000

Just sequentially divide 1000 by 2 until you get no further whole numbers

1000 /2=500

500/2=250

250/2=125 <--------!

125/2=62.5 XXXXXX

ElectricPavlov Sep 21, 2018

#3**0 **

Someone actually gave you a point for this bulllshit. How can you NOT see logarithmic and exponential relationships in a simple question like this, when you answer interest rate questions all the time?

Guest Sep 22, 2018

#4**0 **

LOL

EP, it seems that I’m not the only one who confuses you for the Blarney Banker.

To me, this post is not very consistent with Mr. BB’s style, but we all have our brain-dead moments. These moments are a way-of-life for the forum’s BBs, and rarely is there a discontinuity.

GA

GingerAle
Sep 23, 2018

#2**+2 **

if you start with one layer and double the number of layers with each fold, and noting that

\(2^{10}=1024\)

it's clear that 10 folds is 1024 layers

if you wanted some number of layers that was enormous say N you would find

\(folds = \left \lceil \log_2(N) \right \rceil\)

where

\(\lceil x \rceil = \text{ the least integer }k,~\ni k > x\)

.Rom Sep 21, 2018