RE: Maths problem to solve

21st October 2016, 23:04
(This post was last modified: 21st October 2016, 23:05 by Aractus.)
(21st October 2016, 22:35)Cato Wrote: This is asinine. If for every step you take, 99 more steps are added to the journey you will never complete the journey. If you present math that suggests otherwise, your math is wrong. Inescapable.

Well since a few of you now have suggested this I'll prove that it can complete the journey, and then leave it to you all to figure out how long it will take. We're not always adding 99 more steps as I just pointed out:

START:

0.

Elastic band: 1m

Ant walks 1cm

Distance in front of ant: 99cm

Distance behind: 1cm

Percentage of circumference so-far travelled (1/100): 1%

1.

Elastic band: 2m

Ant walks 1cm

Distance in front of ant: 197cm

Distance behind: 3cm

Percentage of circumference so-far travelled (3/200): 1.5%

2.

Elastic band: 3m

Ant walks 1cm

Distance in front of ant: 294.5cm

Distance behind: 5.5cm

Percentage of circumference so-far travelled (5.5/300): 1.8333... %

3.

Elastic band: 4m

Ant walks 1cm

Distance in front of ant: 391.666... cm

Distance behind: 8.333... cm

Percentage of circumference so-far travelled (8.333.../400): 2.08333... %

...

So you can see the ant is making progress, after 4 seconds he has travelled a little over 2% of the total circumference. That means that less distance is being added in front of him after each second than the previous second. That is, that only the first time was 99cm added in front of the ant, the next time it was stretched only 98.5cm was added, and then the next time only 98.1666... cm was added. So you can see the distance added to his journey each time gets smaller and smaller. So the ant can complete the journey. But you absolutely can't calculate it by hand second by second - if you try to do that believe me you will never find the answer, you need to generalise what's happening into a series and then solve for the nth term of the series (n being the number of seconds).

For Religion & Health see:[/b][/size] Williams & Sternthal. (2007). Spirituality, religion and health: Evidence and research directions. Med. J. Aust., 186(10), S47-S50. -LINK

The WIN/Gallup End of Year Survey 2013 found the US was perceived to be the greatest threat to world peace by a huge margin, with 24% of respondents fearful of the US followed by: 8% for Pakistan, and 6% for China. This was followed by 5% each for: Afghanistan, Iran, Israel, North Korea. -LINK

"That's disgusting. There were clean athletes out there that have had their whole careers ruined by people like Lance Armstrong who just bended thoughts to fit their circumstances. He didn't look up cheating because he wanted to stop, he wanted to justify what he was doing and to keep that continuing on." - Nicole Cooke

The WIN/Gallup End of Year Survey 2013 found the US was perceived to be the greatest threat to world peace by a huge margin, with 24% of respondents fearful of the US followed by: 8% for Pakistan, and 6% for China. This was followed by 5% each for: Afghanistan, Iran, Israel, North Korea. -LINK

"That's disgusting. There were clean athletes out there that have had their whole careers ruined by people like Lance Armstrong who just bended thoughts to fit their circumstances. He didn't look up cheating because he wanted to stop, he wanted to justify what he was doing and to keep that continuing on." - Nicole Cooke