Math BBC Radio Four Today Prog, puzzle of the day.

[Notebook]

UK BBC Radio 4 Today programme is a news/current affairs programme that's been going donkeys years. Starts 06:00 for three hours, later on a Saturday.
Bit of an institution.

For some reason they have started a "puzzle of the day":
http://www.bbc.co.uk/programmes/articles/5wkxjTtqRvq8Cyrrjxtk7tc/puzzle-for-today

If I was paranoid, I'd think it was a recruiting drive for GCHQ, but I know folk here like a challenge.

May be co-incidence, but "book at bed-time" is Fahrenheit 451.

N.

 

[asbjos]

A nice little challenge! I solved it in MATLAB with a small script, which found the 11 different solutions to the problem in 12 seconds on a laptop from 2012.

I won't post the solutions here, because I don't want to ruin the fun for you, but I can say that there are four solutions starting with '1+', two with '12+', one with '12-', two with '123+' and the last two with '123-'. The solution with the lowest number of signs contains two minus signs and one plus sign.

 

[Notebook]

Excellent.

Bit of a wordy one this morning. Too much like hard work for me, but I'm sure lots of people will lap it up.

Any chance you could post your script please?

N.

 

[dgatsoulis]

No plus or minus signs at all?

[math]1^{23456789}=10^0[/math]

 

[asbjos]

I know nested for-loops are not the most beautiful thing in the world, but at least it works.

% Solution on problem on BBC (http://www.bbc.co.uk/programmes/articles/5wkxjTtqRvq8Cyrrjxtk7tc/puzzle-for-today)

filename = sprintf ('BBCsolutions.txt');
filID = fopen(filename, 'w');
tic

for a = 1 : 3
    for b = 1 : 3
        for c = 1 : 3
            for d = 1 : 3
                for e = 1 : 3
                    for f = 1 : 3
                        for g = 1 : 3
                            for h = 1 : 3
                                str1 = signChoice(a, 1);
                                str2 = signChoice(b, 2);
                                str3 = signChoice(c, 3);
                                str4 = signChoice(d, 4);
                                str5 = signChoice(e, 5);
                                str6 = signChoice(f, 6);
                                str7 = signChoice(g, 7);
                                str8 = signChoice(h, 8);
                                
                                str = strcat(str1, str2, str3, str4, str5, str6, str7, str8, '9');
                                
                                if str2num(str) == 100
                                    fprintf(filID,'%s%s%s%s%s%s%s%s9\n', str1, str2, str3, str4, str5, str6, str7, str8);
                                end
                            end
                        end
                    end
                end
            end
        end
    end
end

fprintf (filID, '\nDONE\n');
fprintf (filID, 'Time: %f s\n', toc);
fclose (filID);

And here the signChoice function:

function str = signChoice (a, n)
    if a == 1
        sgn = '+';
    elseif a == 2
        sgn = '-';
    else
        sgn = '';
    end
    
    str = strcat(num2str(n), sgn);
end

 

[kuddel]

A similar problem was presented at numberphile