# Scoring probabilities

*Author: Shlomi Fish*

http://projecteuler.net/problem=286

Barbara is a mathematician and a basketball player. She has found that the probability of scoring a point when shooting from a distance x is exactly (1 - x/q), where q is a real constant greater than 50.

During each practice run, she takes shots from distances x = 1, x = 2, ..., x = 50 and, according to her records, she has precisely a 2 % chance to score a total of exactly 20 points.

Find q and give your answer rounded to 10 decimal places.

Source code: prob286-shlomif.p6

use v6; sub calc($q) { my @probs = (1.0); for 1 .. 50 -> $x { my $p = 1 - $x / $q; my @new_probs; for 0 .. $x -> $i { @new_probs.push( (($i == $x) ?? 0 !! @probs[$i] * (1-$p)) + (($i == 0) ?? 0 !! ($p * @probs[$i-1])) ); } @probs = @new_probs; } return @probs[20]; } sub MAIN(:$verbose = False) { my $l = 50.0; my $h = 100000.0; my $Epsilon = 1e-16; my $wanted = 0.02; BIN_SEARCH: while (1) { my $m = (($l + $h) / 2); my $v_m = calc($m); printf("f(%.40f) = %.40f\n", $m, $v_m); my $delta = abs($v_m - $wanted); # say ("Delta = $delta"); if ($delta < $Epsilon) { last BIN_SEARCH; } if ($v_m > $wanted) { $l = $m; } else { $h = $m; } } }