We write a program that finds a positive n number of integers. So, if all the integers from 1 to n in the form 1 + 2 + 3 + ⋯ + n are summed up, the result is between 100 and 1000. At the same time, the three numbers of this sum are the same (like 333

We write a program that finds a positive n number of integers. So, if all the integers from 1 to n in the form 1 + 2 + 3 + ⋯ + n are summed up, the result is between 100 and 1000. At the same time, the three numbers of this sum are the same (like 333). Print the integer and sum of the program as output.

[James Tursa]

What have you done so far? What specific problems are you having with your code?

Answer 1

[Cam Salzberger]

So you could solve this with a complete brute-force method, but let's not because that's no fun. If I were to approach this problem, I would first check out what the mathematical expression is for 1+2+...+n. There's a convenient Wikipedia article on this showing that it's n(n+1)/2.

So now you know that given the total value, you can solve for the roots of this equation to get n:

0 = (n^2 + n -2*total)

or

n = roots([1 1 -2*total])

And you know your desired possible total values (111, 222, ..., 999). So if I were doing this just in the Command Window, I would run that through a loop, solving for n for each value:

s = [111 222 333 444 555 666 777 888 999];
for k = 1:length(s)
    roots([1 1 -2*s(k)])
end

And then just see which of the (positive) n values was an integer. Double-check this with sum(1:n).

Now to automate it, you'd just have to automate the finding of which value is an integer. This is pretty simple to do with mod or floor, so I'll leave it to you.

Hope this helps!

-Cam

Answer 2

[ramazan araz]

What does the 'tal' that you use in the beginning cover?

[Cam Salzberger]

I didn't use 'tal' anywhere, so I assume you are talking about "total". This is representing the "all summed up" value in the question. For this case, we know we want the total to be 111, 222, 333, ..., or 999.

[John D'Errico]

Please don't add an answer just to make a comment. As you see, it is very simple to make a comment. Use that instead.