A person starts from zero and initially has a step size of 1. After each step, the step size increases by 1. E.G. From 0, he can go to 1 or -1 with step size of 1. From 1 he can go to to -1 or 3 as the step size has become 2 now and so on. Find minimum no. Of steps to reach a given number n.
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There are two cases :
The man should walk one step backward and then one step forward which gives resultant one number lead ahead So to reach n he had to go back and front : n+n-1 times which is (2n-1). So minimum steps required is (2n-1) as each of his step is increasing in magnitude.
The above answer is only valid until n is not among : 1,3,6,10,15,21... which are sum of first n numbers. In this case the man requires only n steps in forward direction.
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