Comments on: Fat Aunts http://yaniv.leviathanonline.com/blog/riddles/fat-aunts/ Strain your Brain Tue, 31 Aug 2010 17:39:33 -0700 hourly 1 http://wordpress.org/?v=3.0.1 By: Nadav http://yaniv.leviathanonline.com/blog/riddles/fat-aunts/comment-page-1/#comment-21229 Nadav Sat, 16 Jan 2010 23:30:39 +0000 http://yaniv.leviathanonline.com/blog/riddles/fat-aunts/#comment-21229 and one small correction: instead of g[t] is smaller and h[t] is greater, i meant to write: f(g[t]),f(h[t]) and one small correction:
instead of g[t] is smaller and h[t] is greater, i meant to write:
f(g[t]),f(h[t])

]]> By: Nadav http://yaniv.leviathanonline.com/blog/riddles/fat-aunts/comment-page-1/#comment-21228 Nadav Sat, 16 Jan 2010 23:29:42 +0000 http://yaniv.leviathanonline.com/blog/riddles/fat-aunts/#comment-21228 Trying to sleep, is the ultimate time for solving riddles. Trying to sleep, is the ultimate time for solving riddles.

]]> By: Nadav http://yaniv.leviathanonline.com/blog/riddles/fat-aunts/comment-page-1/#comment-21227 Nadav Sat, 16 Jan 2010 23:28:52 +0000 http://yaniv.leviathanonline.com/blog/riddles/fat-aunts/#comment-21227 Solution: It is impossible for the aunts to exchange houses. Proof: Mark route 1 as p:[0,1] to R^n (n is the map's dimension, 2 in this case) Mark route 2 as q:[0,1] to R^n (n is the map's dimension, 2 in this case) Consider the following function f:[0,1]x[0,1] to R f(x,y)=dist(p(x),q(y)) f is the distance from each point on route 1 to each point on route 2. Given the fact that the aunts could walk with the rope, we get that there is a path g:[0,1] to [0,1]x[0,1] such that: g[0] = (0,0) g[1] = (1,1) g[t] is smaller than L the aunts could exchange houses, iff there is a path h:[0,1] to [0,1]x[0,1] such that: h[0] = (1,0) h[1] = (0,1) h[t] is greater than L ofcourse h and g must intersect, therefore it is impossible Solution:
It is impossible for the aunts to exchange houses.

Proof:
Mark route 1 as p:[0,1] to R^n (n is the map’s dimension, 2 in this case)
Mark route 2 as q:[0,1] to R^n (n is the map’s dimension, 2 in this case)

Consider the following function f:[0,1]x[0,1] to R
f(x,y)=dist(p(x),q(y))

f is the distance from each point on route 1 to each point on route 2.

Given the fact that the aunts could walk with the rope, we get that there is a path g:[0,1] to [0,1]x[0,1]
such that:
g[0] = (0,0)
g[1] = (1,1)
g[t] is smaller than L

the aunts could exchange houses, iff there is a path h:[0,1] to [0,1]x[0,1] such that:

h[0] = (1,0)
h[1] = (0,1)
h[t] is greater than L

ofcourse h and g must intersect, therefore it is impossible

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