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B - is my answer.
ReplyDeleteSuch a simple problem, and the correct answer isn't even listed as an option!
ReplyDeleteF) 3*sqrt(2)/4
Hint: Checkerboard
-DM
Probability of each distance case:
ReplyDelete* Distance 0: 25%
* Distance 1: 0%
* Distance sqrt(2): 75%
* Distance sqrt(3): 0%
Average distance = 3*sqrt(2)/4 = approx. 1.061
The Perl source code of my simulation program is shown below.
ReplyDelete#!/usr/local/bin/perl
$N = 1000;
$f = 100/$N;
$sum = 0;
%sums = (0, 0, 0, 0);
($x1, $y1, $z1) = (0, 0, 1);
($x2, $y2, $z2) = (1, 1, 1);
%vectors = (
"0,0,0", [[1,0,0],[0,1,0],[0,0,1]],
"0,0,1", [[1,0,0],[0,1,0],[0,0,-1]],
"0,1,0", [[1,0,0],[0,-1,0],[0,0,1]],
"0,1,1", [[1,0,0],[0,-1,0],[0,0,-1]],
"1,0,0", [[-1,0,0],[0,1,0],[0,0,1]],
"1,0,1", [[-1,0,0],[0,1,0],[0,0,-1]],
"1,1,0", [[-1,0,0],[0,-1,0],[0,0,1]],
"1,1,1", [[-1,0,0],[0,-1,0],[0,0,-1]]);
MAIN: {
my $d;
for ($i=0; $i<$N; $i++) {
$d = abs($x1-$x2)+abs($y1-$y2)+abs($z1-$z2);
$sums[$d]++;
$sum += sqrt(($x1-$x2)**2 + ($y1-$y2)**2 + ($z1-$z2)**2);
($x1,$y1,$z1) = &get_next($x1,$y1,$z1);
($x2,$y2,$z2) = &get_next($x2,$y2,$z2);
}
printf("Average distance: %.2f\n", $sum/$N);
printf("(0: %.0f%) (1: %.0f%) (sqrt(2): %.0f%) (sqrt(3): %.0f%)\n",
$sums[0]*$f, $sums[1]*$f, $sums[2]*$f, $sums[3]*$f);
}
sub get_next() {
my ($x,$y,$z) = @_;
my ($dx,$dy,$dz);
my $index = int(rand(3));
my $key;
$key = sprintf("%d,%d,%d", $x, $y, $z);
$x += $vectors{$key}->[0][$index];
$y += $vectors{$key}->[1][$index];
$z += $vectors{$key}->[2][$index];
return($x,$y,$z);
}
Do not use all of these Private Money Lender here.They are located in Nigeria, Ghana Turkey, France and Israel.My name is Mrs.Ramirez Cecilia, I am from Philippines. Have you been looking for a loan?Do you need an urgent personal or business loan?contact Fast Legitimate Loan Approval he help me with a loan of $78.000 some days ago after been scammed of $19,000 from a woman claiming to be a loan lender from Nigeria but i thank God today that i got my loan worth $78.000.Feel free to contact the company for a genuine financial call/whats-App Contact Number +918929509036 Email:(fastloanoffer34@gmail.com)
ReplyDelete