Solution: Bulb Switcher

Statement▼

You are given n bulbs, all initially turned off. You perform n rounds of toggling operations:

In round $1$ , you turn on every bulb.
In round $2$ , you toggle every $2^{nd}$ bulb.
In round $3$ , you toggle every $3^{rd}$ bulb.
In general, during round i, you toggle every i-th bulb (turning it on if it is off, or turning it off if it is on).
In round n, you toggle only the last bulb.

Return the number of bulbs that remain on after all n rounds have been completed.

Constraints:

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Solution

You are given n bulbs, all initially turned off. You perform n rounds of toggling operations:

In round $1$ , you turn on every bulb.
In round $2$ , you toggle every $2^{nd}$ bulb.
In round $3$ , you toggle every $3^{rd}$ bulb.
In general, during round i, you toggle every i-th bulb (turning it on if it is off, or turning it off if it is on).
In round n, you toggle only the last bulb.

Return the number of bulbs that remain on after all n rounds have been completed.

Constraints: