Moment of Inertia [ Hiran ]

Solution to yesterday's problem

Solution to yesterday's problem:

45818999
x      2
--------
91637998

and the corresponding ruby code:

i = 10000000
while(i < 50000000)
        i_str = i.to_s
        product = (i*2).to_s
        ight = [product[1].chr, product[2].chr, product[3].chr, product[4].chr]
        if( (i_str[2].chr == i_str[4].chr) and
                (i_str[2].chr != "9") and
                (i_str[3].chr == product[1].chr) and
                (i_str[2].chr == product[-1].chr) and
                (product[0].chr == product[-2].chr) and
                (product[0].chr == product[-3].chr) and
                (i_str[-3].chr == product[-2].chr) and
                (ight.uniq.length == ight.length) and
                (ight & [product[-1].chr]).empty?
        )
                p [i, product.to_i]
        end
        i += 1
end

The logic is pretty much straight forward.

New Scientist - Enigma and Puzzles

Solving puzzles have always been my first choice of entertainment, given the condition that I am sitting jobless, which has not happened after joining here. But of late, I have been giving some time for myself, and that is helping me in my work also. Now that I am staying in a fully furnished house, I spend time at home solving puzzles while watching Kiran TV (ohh!! I love that channel).

4 days back, I came across a puzzle

* * N I N E * *
x                  2
-----------------
E I G H T E E N

This will be familiar for folks who underwent a course on Artificial Intelligence during their graduation. I thoroughly enjoyed solving this problem, since this was much better (tougher) problem than those faced during the course. I solved this in roughly 4 hours, by putting together, the process of elimination and trial-n-error methods. Well, I could have saved time, by writing a ruby code for the same instead of solving manually. But then where is the fun?

Now that I have the solution, I can implement a ruby code and see how much time it actually takes me to solve the problem.

Solution in my next post.

The Cow and the Milk

The USDA once wanted to make cows produce milk faster, to improve the dairy industry.
So, they decided to consult the foremost biologists and recombinant DNA technicians to build them a better cow. They assembled this team of great scientists, and gave them unlimited funding. They requested rare chemicals, weird bacteria, tons of quarantine equipment, there was a horrible typhus epidemic they started by accident, and, 2 years later, they came back with the ,,new, improved cow``. It had a milk production improvement of 2% over the original.

They then tried with the greatest Nobel Prize winning chemists around. They worked for six months, and, after requisitioning tons of chemical equipment, and poisoning half the small town in Colorado where they were working with a toxic cloud from one of their experiments, they got a 5% improvement in milk output.

The physicists tried for a year, and, after ten thousand cows were subjected to radiation therapy, they got a 1% improvement in output.

Finally, in desperation, they turned to the mathematicians. The foremost mathematician of his time offered to help them with the problem. Upon hearing the problem, he told the delegation that they could come back in the morning and he would have solved the problem. In the morning, they came back, and he handed them a piece of paper with the computations for the new, 300% improved milk cow.

The plans began: ,,A Proof of the Attainability of Increased Milk Output from Bovines: Consider a spherical cow...``

That is from here.

Interesting right? Well that gives a small idea on how to speculate problems in a mathematical way....!!

Enigma - 1412

A similar problem, one would have solved during one's CS course on AI.

#Problem Statement



AMOUNT - AN = ANY * ANY



and



(TOTAL + ANY)/A = a whole number

Find A,M,O,U,N,T,Y,L where each are distinct digits. Then what will be VALUE.

This is my program, and my VALUE is 89140.

The program is a type of brute-force method. Solving using predicate logic is tougher.

New Scientist - Enigma 1405

`Enigma' puzzles in `New Scientist' is really fun to solve. The current one which i just solved is `Digitally Divided Sum'. I am not posting the problem statement, which I am not sure, I can due to `Copyright' laws. But I can post the solution. :-) So here is my ruby code for that. Though not optimized, it gives a solution.

#Reverse engineer the problem statement

def get_digits(i)

  tmp = Array.new

  i.to_s.each_byte {|x|

    tmp.push(x.chr.to_i)

  }

  return tmp

end



def is_divisible_by_its_digits(i)

  list = get_digits(i)

  if list.uniq != list

    return false

  end

  list.each {|x|

    if i%x != 0

      return false

    end

  }

  return true

end



def get_n_digit_list(start_no, end_no)

  list = Array.new

  while start_no < end_no

    if start_no.to_s.include?("0") == false

      if is_divisible_by_its_digits(start_no) == true

        list.push(start_no)

      end

    end

    start_no += 1

  end

  return list

end



def has_uniq_digits(a, b, c)

  list = Array.new

  list = get_digits(a)

  list += get_digits(b)

  list += get_digits(c)

  if list.uniq == list

    return true

  else

    return false

  end

end



def main()

  digit2 = get_n_digit_list(10, 100)

  digit3 = get_n_digit_list(100, 1000)

  digit4 = get_n_digit_list(1000, 10000)

  digit4.each{|dig4|

    digit3.each{|dig3|

      digit2.each{|dig2|

        if has_uniq_digits(dig2, dig3, dig4) == true

          sum = dig2+dig3+dig4

          if sum < 10000

            if sum.to_s.include?("0") == false

              if is_divisible_by_its_digits(sum) == true

                list = get_digits(sum)

                if list.uniq == list

                  p "#{dig2} + #{dig3} + #{dig4}"

                  return

                end

              end

            end

          end

        end

      }

    }

  }

end



main()

So what is the result?