gistfile1.matlab

%% 2.2.20 BREAKS

n = 10^5;

breaks = rand(n,2);
maxbreak = max(breaks')';
minbreak = min(breaks')';

triangles = and(and(minbreak <.5, (1-maxbreak<.5)), (maxbreak - minbreak) < .5);
sum(triangles)/n


%% 3.1.22 - GUESS THE NUMBER OF WATCHES

% parameters
true_max = 100;
numfound = 16; 
reps = 10^4; 

% shuffle the watches around
shuffle = @(n) randperm(n);
watches = cell2mat(arrayfun(shuffle, ones(1,reps)*true_max, 'UniformOutput',false)');

% select a subset of the watches
found_watches = watches(:,1:numfound);
max_watch = max(found_watches');

% come up with guesses
watsons_guess = max_watch;
holmes_guess = max_watch*2;

% measure the average distance from the truth
dif = @(g) sum(abs(true_max -g))/reps;
watson = dif(watsons_guess)
holmes = dif(holmes_guess)



%% 3.1.24 - CANDIDATES
n = 10;
k = 3; 
reps = 10^4;

shuffle = @(n) randperm(n);
applicants = cell2mat(arrayfun(shuffle, ones(1,reps)*n, 'UniformOutput',false)');
applicants = [applicants, ones(reps,1)*(n+1)];

max_left = max(applicants(:, 1:k)')';
right_side = applicants(:,(k+1):end);

best = @(ex) find(right_side(ex,:)>max_left(ex), 1);

count = 0;
for i = 1:reps
  [r,c,v]=  best(i);
  if right_side(i,c) == 10
    count = count + 1;
  end
end
count/reps