Question 70
There are $10000$ light bulbs numbered from $1$ onwards, each of which is turned on and off with an ordinary switch. At the beginning all bulbs are off; then the switches of all the bulbs marked with multiples of $1$ are pressed once (consequently all the bulbs are turned on), next the switches of all those in even position (that is, multiples of $2$) are pressed once, then those marked with multiples of $3$, next the state of those corresponding to multiples of $4$ is changed, and so on, up to the multiples of $10000$. Which of the following bulbs remains on at the end of the operations?
(A) Bulb number $9405$
(B) bulb number $9406$
(C) bulb number $9407$
(D) bulb number $9408$
(E) bulb number $9409$.
(A) Bulb number $9405$
(B) bulb number $9406$
(C) bulb number $9407$
(D) bulb number $9408$
(E) bulb number $9409$.