How should I scratch this ticket?

One of our local car dealers is having a promotion where they give out scratch tickets. The rules are simple - scratch any six boxes on the 5 by 5 grid and if they all contain a $ sign then you win some money.

http://dropdo.com/4We/ticket

The challenge: come up with a MATLABish way to generate six unique linear indices from 1:25. Any algorithm, method, implementation is okay. The results; however, need to be repeatable when run on my system. This could be as simple as:

luckyN = @()[1 11 18 22 13 3]; %your choice lucky numbers

to anything way more complicated than I can't understand. Points for originality. Explain what you're doing so this can be sort of educational.

The winner will get an answer acceptance, and if their numbers win, something even cooler. You have until Monday June 27th at 1700 EDT. Multiple answers okay as well :)

The Results:

[the cyclist]

What version of MATLAB are you running? Also, by "repeatable", do you mean just that the code has to run, or that you get the same sequence of numbers as I do every time you run it?

[Sean de Wolski]

2009b, so yes, I don't have rng. However, this may force me to upgrade to 2011 today, or I might be able to find a machine here with it.

By repeatable I meant reproducible numbers; but I think that kind of takes some of the fun out of it so I may strike that as a requirement. What's the consensus on that?

[Sean de Wolski]

I'll try and fix the quality of the result as well as post the mfile.

Answer 1

[Andrew Newell]

ceil(datevec(exp(1)))+1

Answer 2

[Paulo Silva]

function easymoneypj
figure %create a new figure
axis([1 6 1 6]) %set the axis min and max values
set(gca,'Color',[0.5 0.9 0.5]) %select the background color (light green)
set(gca,'xtick',[]) %hide the x ticks
set(gca,'ytick',[]) %hide the y ticks
set(gca,'YDir','reverse') %reverse the y direction, now it's similar to array
hold on %retain the current plot and certain axes properties 
title('Good Luck') %set the title of the axis
%create the pushbutton, it's used to select another group of random numbers
pbh1 = uicontrol(gcf,'Style','pushbutton','String','New ticket',...
    'Position',[10 40 60 40],...
    'callback',@newcomb);
%create the textbox to show the numbers
tx = uicontrol(gcf,'Style','text','String','',...
    'Position',[10 10 600 30],'FontSize',20);
newcomb %call the function to create random numbers when GUI starts 
    function newcomb(obj,ev) %this function create the random numbers
        x = randperm(25); %returns a random permutation of the integers 
        %select the first 6 random integers
        pick=x(1:6) %stolen code from the cyclist :) hope you don't mind
        %show the random integers on the GUI textbox
        set(tx,'String',num2str(pick)) %thanks
        cla %delete from the current axes all graphics objects
        %create the grid lines
        for n=1:4
            line(n+ones(6,1),1:6)
            line(1:6,n+ones(6,1))
        end
        %draw one X on each of the six squares 
        for n=1:6
            p=pick(n); %get each of the first 6 random integers
            [x y]=ind2sub([5 5],p); %get their row and column
            text(x+0.3,y+0.4,'x','FontSize',50) %put the X on the spot
        end
    end
end

%

[Andrew Newell]

I could watch this for minutes! (Sorry, short attention sp

[the cyclist]

I don't mind your "stealing" my code, but I should get a small share of your winnings if you get any! :-)

[Paulo Silva]

You can keep half of the prize :)

[Fangjun Jiang]

Paulo, the rule says you need to hit 6 '$', not 6 'X'!

[Paulo Silva]

Those X just mark the spot where the $ is, you have to scratch to see the $

[Fangjun Jiang]

Good answer! I though I could gotcha.

Answer 3

[bym]

here goes

find(magic(5)<7)

Answer 4

[the cyclist]

rng(1); % Latest and greatest for setting the seed. (Only works on newest version of MATLAB.)
x = randperm(25);
pick=x(1:6)

[the cyclist]

Sorry, I accidentally wrote "png" for seed-setting when I submitted this. Just noticed that now.

Answer 5

[Matt Fig]

function [R,cnt] = winning_numbers()
% Generates 6 winning numbers on [1 25] and returns a seed to the 
% twister algorithm which guarantees that the numbers are members of a 
% consecutive set.

cnt = 1;
R = [];

while length(R)<6
    rand('twister',cnt);
    R = ceil(rand*25);
    for ii = 2:6
        R(ii) = ceil(rand*25);
        if ~all(diff(sort(R))==1)
            R = [];
            break
        end
    end
    cnt = cnt+1;
end
cnt = cnt-1;

Answer 6

[Fangjun Jiang]

Very often, I got scratch pad from banks or local retail stores. Here is my entry. Hope your auto dealer has the same best spirit.

Ticket=repmat('$',5,5);
WinningNumber=find(Ticket=='$',6);

[Andrew Newell]

Thematically appropriate!

Answer 7

[David Young]

I think that for such a hard problem, a collaborative solution is needed.

% Collect expert opinion on the topic
answers = urlread('http://www.mathworks.com/matlabcentral/answers/10272-how-should-i-scratch-this-ticket');
% Strip out everything except the body of the answers
answercells = regexp(answers, '<div class="answer_body" id="answer_\d+_body">(.*?)</div>', 'tokens');
% Merge the answers into a long string
answerstrings = cellfun(@(c) c{1}, answercells, 'UniformOutput', false);
answersString = [answerstrings{:}];
% Pick out the numbers from this string. Assume that if someone has put a
% number in their answer, they think it's lucky
lucky_numbers = str2num(regexprep(answersString,'[^0-9]+', ' '));
% Some of these lucky numbers must be for other kinds of game, so get rid
% of them
right_lucky_numbers = lucky_numbers(lucky_numbers >= 1 & lucky_numbers <= 25);
% Now choose the 6 luckiest numbers according to the votes given by the
% experts
h = hist(right_lucky_numbers, 1:25);
[~, sorted_lucky_numbers] = sort(h, 'descend');
luckiest_numbers = sorted_lucky_numbers(1:6)

Answer 8

[Sean de Wolski]

My own idea; thought of from a thread yesterday:

function [idx nreps] = luckyN
%Function to pick which numbers will give me the most $$.
%
%Method:
%   Seed the twister to every integer between 1 and a million.  Generate 25
%   random numbers and sort them.  The indices of the six lowest numbers
%   are that seed's winners.  The combo with the most repetitions wins
%
%
%Outputs:
%   -idx: six unique integers from 1 to 25
%   -nreps: just for fun - how many times did it occur?
%

combos = zeros(1000000,6);
for ii = 1:1000000
  rand('twister',ii) 
  [~,ndxs] = sort(rand(1,25));
  combos(ii,:) = ndxs(1:6);
end
[~,~,reps] = unique(combos,'rows');
[nreps,windex] = max(accumarray(reps,1));
idx = combos(windex,:);

Answer 9

[Andrew Newell]

mod('I win!',25)

Here is another variant that gets to the point:

Scratch_what = mod('itches',25);

Answer 10

[Paulo Silva]

figure
axes('xlim',[0 7],'ylim',[0 10])
nr=zeros(1,6);
for n=1:6
    m=1;
    h=text(n,m,'1');
    while m<=8
        set(h,'Position',[n,m])
        nr(n)=randi([1 25]);
        set(h,'String',num2str(nr(n)))
        if sum(ismember(nr,nr(n)))<2 %if already selected ignore it
            pause(0.2) %speed of the animation, pause 0.2 seconds by default
            m=m+1;
        end
    end
end
nr

Answer 11

[the cyclist]

% Inefficiently choose by tumbling through product space
  luckyN = zeros(1,5);
 N=2000; % Choose larger N for more suspense
  while not(length(unique(luckyN))==5 && all(luckyN>=1) && all(luckyN<=25))
      luckyN=round(randn(1,N)*randn(N,5)); % Remove semicolon to watch the process
  end

luckyN

Answer 12

[the cyclist]

sum(toeplitz(5:-1:1,-2:2))

Answer 13

[the cyclist]

This one gives you a choice of two lucky sequences. Both the input and output are lucky.

luckyIn = [1 2 3 4 5 6] % Fixed, after comment from Fangjun Jiang
luckyOut = sum(hankel(luckyIn))

[Fangjun Jiang]

cyclist, you won't be lucky if you don't hit 6!

[Andrew Newell]

You're keeping us honest, Fangjun!

Answer 14

[Jan]

With FEX: Shuffle:

Shuffle(25, 'index', 6)

But let me read original rules again more carefully:

 scratch any six boxes on the 5 by 5 grid and
 if they all contain a $ sign

Your formulation "generate six unique linear indices from 1:25" does not match these rules exactly: There is no restriction, that I have to choose 6 different boxes. The chance that all boxes contain a $ sign is (number of $ / 25) if I choose the same box 6 times. Then one of the optimal algorithms is:

index = repmat(19, 1, 6)

See also: CSSM: 9 Sep, 2010 13:29:09:

Carl E. Linderholm: "Each sequence of natural number can be continued by 19."