# Puzzles_Probability

#1

There are 100 bulbs lined up in a room. All are turned on in the first pass. Then all the even numbered light bulbs are switched off. After that, every third bulb is switched on. Then all those bulbs that were switched off are turned back on and all those that were lit are turned off. Then the same process is being carried with the fourth bulb and the fifth bulb.

How many bulbs are glowing after 100 passes?

#2

10 bulbs.

for this puzzle,you must check how many light bulbs in the row are having an odd number of factors.the first one surely has odd number of factors,the second has even,four has odd.thus the bulb four and one will remain lit.the bulbs that are going to remain lit are perfect squares as they have an odd number of factors-1,4,9,16.

since there are 100 passes,you can go up to 10 times 10 i.e.the square of 10.there are 10 perfect squares available to you-one,two,three,four,five,six,seven,eight,nine,ten.they corresponds to the bulb number1,4,9,16,25,36,49,64,81 and 100.all of them will remain lit and thus the total ten bulbs will remain lit after 100 passes.