*Answer to last puzzle: Yes, the arrow will meet its mark, because it is possible for an infinite summation of numbers to equal a finite sum. In other words, we can add the "half distances" infinitely many times, and it can produce a finite "total distance".*

Although it has its foundation backed by mathematics, I don't like this answer! Some of the answers I received in the comments were much more intriguing and founded in physics roots or other more tangible properties:

*"The number gets so small that it is good enough to be called touching. besides. Due to the fact that atoms exert a force on other atoms nothing ever really touches anything. we only experience the forces of the atoms pushing on one another."*-vashrave

*"I would say no as even if it is halved to infinity, it would eventually be traveling a distance of Planck length(1.163*10^-35).*

IE: Much smaller than a neutrino which is so tiny that it can pass through matter almost undisturbed. Strings(1D) in String theory exist at this level.

Any length shorter than Planck length makes no sense given the laws of physics and quantum mechanics that are agreed upon by the scientific community today."-Mike

IE: Much smaller than a neutrino which is so tiny that it can pass through matter almost undisturbed. Strings(1D) in String theory exist at this level.

Any length shorter than Planck length makes no sense given the laws of physics and quantum mechanics that are agreed upon by the scientific community today."

*"I thought its a simple limit of a geometric series. Mathematically, the formula for the series of each halving of the distance will be 5/(2^n) from n=0 to n=infinity. As |r| < 1 the series diverges and the entire distance traveled is the sum of this series. The formula for the entire distance traveled is a/(1-r) where a=5 and r=0.5 (from 5/(2^n)) So the total distance traveled is 5/(1-0.5)=10. Sorry if this is hard to follow, it made more sense in my brain."*-TheGeneral

TheGeneral's was probably the closest to my mathematical explanation. In response to Jacob who said,

*"Good rule If you have a roommate; Take no more than half the sugar.. that way there will ALWAYS be some left^^"*This isn't exactly true, because eventually you'll reach the last grain which you can't half (not easily, anyway). In other words, there's a fundamental unit; time and space, on the other hand (as the question is composed of) has no fundamental unit so it can be infinitely halved. Nice try though, Jacob =).

*You are given four large wooden letters on a table in front of you. They are the lower case "a", the lowercase "n", the lowercase "t", and the lowercase "h". Arrange these letters to make a hexagon. You may not use a curved side as a straight side.*

h

ReplyDeletea t

n

I can't seem to figure it out.

first put a and n, together, then place the h below, the add the t on top, then FUUUUUUUUUUUUUUUUUUUUUUUUUUUUU!!!!

ReplyDeleteAha, now the pieces fell together

ReplyDeleteWell that's tricky cos my a's are all curved

ReplyDeletehard one

ReplyDeletemy "a"'s all curved, too. HALP

ReplyDeleteTake a saw, cut all the pieces you don't need like the curved parts. Finnally find some glue and make your hexagone. VoilĂˇ!

ReplyDeleteTricky one

ReplyDeleteYou always know how to make me feel really dumb... Why do I only ever read your blog when I've either just woken up or am just about to go to sleep?

ReplyDeleteI just found this blog and I am going to be here every day from now on. Stupid addiction to puzzles.

ReplyDeletehard!

ReplyDeletehttp://le-nerd.blogspot.com/

The a really makes things interesting, I'm pretty positive the trick here is thinking outside of the box, but I can't see it.

ReplyDeleteCool post, bro!

ReplyDeleteHahahhaha. Great post! I love this blog!!!! Don't forget about me man :)

ReplyDeletewww.neverboringnews.blogspot.com

this is really messing up my brain i dont think my brain has ever computed this much

ReplyDeleteBrain =

ReplyDeleteNeed to reread. Maybe I should come back after the caffeine kicks in!

i love your posts!

ReplyDeleteMehh, not easy.

ReplyDeleteMy mind hurts now!

ReplyDeletei would chop up the letters and do it

ReplyDeleteI cannot wait to hear the answer for this because I have no idea

ReplyDeleteThe answer is thirty seven!

ReplyDeleteI...don't know

ReplyDeleteyou're wrong the answer is always 2!

ReplyDelete