[TwoOfDiamonds]

Ok, so I was looking at some exam problems that are given in order to get into a certain college. And I could solve them all but one , you can consider this a challenge if you like (please use spoiler tags) . Also, it requires only the algorithm so you should provide it in pseudocode.

Data: You are the following sequence of numbers 1,2,2,3,3,3,4,4,4,4,... Basically each number repeats itself accordingly to its value .
Requirement: Provide an algorithm that will return the Nth element of the sequence ( N will be given by input ) . The algorithm must run in a constant time ( it should not depend on the value of N )

I tried some wild ideas but it didn't work so far , so please have a try. Enjoy solving !

[modi123_1]

Interesting way to crowd source an exam answer. Have you thought about just two for loops and a counter?

[DarenR]

put the thing in a loop and have the number become the increment variable. then also have the number in the loop to print the variable as many times as the loop runs.

[TwoOfDiamonds]

Actually the solution looks like this .

Since the numbers go like 1, 2, 2, 3, 3, 3, 4, 4, 4, 4,etc.
We can write n like this:

x(x+1) / 2 = n then we find out how much x is and so we'll have a_n = x if x is integer and a_n = [x] + 1 if x is float .