There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 people lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. So is each person. Person No. 1 enters the room, switches on every bulb, and exits. Person No. 2 enters and flips the switch on every second bulb (turning off bulbs 2, 4, 6, ...). Person No. 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9, ...). This continues until all 100 people have passed through the room. What is the final state of bulb No. 64? And how many of the light bulbs are illuminated after the 100th person has passed through the room? -Riddles

There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 people lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. So is each person. Person No. 1 enters the room, switches on every bulb, and exits. Person No. 2 enters and flips the switch on every second bulb (turning off bulbs 2, 4, 6, ...). Person No. 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9, ...). This continues until all 100 people have passed through the room. What is the final state of bulb No. 64? And how many of the light bulbs are illuminated after the 100th person has passed through the room? -Riddles
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1 Answer

Answer :

First think who will operate each bulb, obviously person #2 will do all the even numbers, and say person #10 will operate all the bulbs that end in a zero. So who would operate for example bulb 48: Persons numbered: 1 & 48, 2 & 24, 3 & 16, 4 & 12, 6 & 8 ........ That is all the factors (numbers by which 48 is divisible) will be in pairs. This means that for every person who switches a bulb on there will be someone to switch it off. This willl result in the bulb being back at it's original state. So why aren't all the bulbs off? Think of bulb 36:- The factors are: 1 & 36, 2 & 13, 6 & 6 Well in this case whilst all the factors are in pairs the number 6 is paired with it's self. Clearly the sixth person will only flick the bulb once and so the pairs don't cancel. This is true of all the square numbers. There are 10 square numbers between 1 and 100 (1, 4, 9, 16, 25, 36, 49, 64, 81 & 100) hence 10 bulbs remain on.
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Related questions

There is a lamp inside a photography darkroom. When the darkroom door is closed, it is impossible to tell from outside the room whether or not the lamp is on. There are two switches outside the door of the darkroom. One or both of the switches may control the lamp. It also could be that neither of the switches control the lamp. All you know is that the light bulb is currently off and that the lamp and bulb are in working condition. The darkroom door is closed and once you open the door you cannot touch either of the switches. If you can only open the dark-room door one time, how can you tell which switches, if any, control the lamp? -Riddles

Description : There is a lamp inside a photography darkroom. When the darkroom door is closed, it is impossible to tell from outside the room whether or not the lamp is on. There are two switches outside the door of ... dark-room door one time, how can you tell which switches, if any, control the lamp? -Riddles

Last Answer : Turn the first switch on and leave it on for ten minutes. After ten minutes, turn that switch off and turn the second switch on. Open the darkroom door, and lightly (in case it is hot) touch the ... one controls the lamp. If the lamp is off, and the bulb is cool, neither switch controls the lamp.

there are 3 light bulbs in three seperate rooms. in front of you, there is a panel with 3 seperate switches. they only turn on or off. you may look inside each room only once. how can you tell which bulb belongs to which switch? -Riddles

Description : there are 3 light bulbs in three seperate rooms. in front of you, there is a panel with 3 seperate switches. they only turn on or off. you may look inside each room only once. how can you tell which bulb belongs to which switch? -Riddles

Last Answer : you turn on any two switches, leave them for a few minutes, and turn one off. you enter each room only once. you know that the lightbulb that is lit beongs to the switch that was left on, the ... hot, belongs to the switch you turned off, and the cold bulb belongs to the switch you never touched.

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Last Answer : He waits until night time and then goes through the first door.

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Last Answer : Answer : D

When light enters a closed room through a small hole in the door, the image of an outside building appears as inverted on the opposite wall. This is because (a) The hole acts as a convex lens (b) Light takes curvature at the edges of the hole (c) Of rectilinear propagation of light (d) The hole acts as a concave lens

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Last Answer : ANSWER: Y -- HEAT UP.

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A man walked into a room, and there were three doors. The first door had a sign which read 'Lion's Den.' The second door had a sign which read 'Mountain Top.' The third door had no sign, yet the man knew exactly where it went. How is that possible? -Riddles

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Last Answer : The third door is the door that the man entered through.

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Last Answer : Answer: D

A boy presses a side of a blue pencil to a side of a yellow pencil, holding both pencils vertically. One inch of the pressed side of the blue pencil, measuring from its lower end, is smeared with paint. The yellow pencil is held steady while the boy slides the blue pencil down 1 inch, continueing to press it against the yellow one. He returns the blue pencil to its former position, then again it slides down 1 inch. He continues until he has lowered the blue pencil 5 times and raised it 5 times- 10 moves in all.Supposed that during this time the paint neither dries nor diminishes in quantity. How many inches of each pencil will be sneared with paint after the tenth move? -Riddles

Description : A boy presses a side of a blue pencil to a side of a yellow pencil, holding both pencils vertically. One inch of the pressed side of the blue pencil, measuring from its lower end, is smeared ... in quantity. How many inches of each pencil will be sneared with paint after the tenth move? -Riddles

Last Answer : At the start, 1inch of the yellow pencil gets smeared with wet paint. As the blue pencil is moved downward, a second inch of the blue pencils smears a second inch of the yellow pencil. Each pair ... of moves will smear 5 inches. This together with the initial inch, makes 6 inches for each pencil.

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Description : A highschool has a strange principal. on the first day of school he does something weird. There are 1000 lockers and 1000 students. He tells the first student to open every first locker. The second student ... this until all the students have done it. How many lockers are open at the end? -Riddles

Last Answer : 31 lockers.

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Last Answer : C

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A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first

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Description : There are three doors. In each door is a way to die. The first door has fire and lava. The second door has lions that haven't eaten in 5 years. In the third door there is a 1,000 foot drop into alligators. Which door will you likely survive? -Riddles

Last Answer : The second door with the lions. Since they haven't eaten in 5 years they will have died.

A ________network is made of a set of switches connected by physical links, in which each link is divided into nchannels. A) line-switched B) frame-switched C) circuit-switched D) none of the above

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Last Answer : circuit-switched

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Description : A son went to his father's house and knocked on the door. When his father answered the door, the son said, 'O.K., today is the day I promised to burn your house to the ground.' 'But I ... 'Well, I guess you're right,' said his father. The son then promptly escorted his father outside, wh -Riddles

Last Answer : The father, although he owned a fully functioning home, had never been able to break himself from the habit of going to the bathroom in the Outhouse he had built for his family back in 1941. The son, ... the son had been trying for some time to get his father to agree to let him burn it down.

As part of a routine maintenance program for deck machinery, you should ___________. A. inspect electrical wiring and pushbutton switches for evidence of corrosion or burned insulation B. disassemble pushbutton switches and drain water each week C. remove motor covers and ventilate as weather permits D. Check drum switch contact pressure every three months

Description : As part of a routine maintenance program for deck machinery, you should ___________. A. inspect electrical wiring and pushbutton switches for evidence of corrosion or burned insulation B. disassemble ... covers and ventilate as weather permits D. Check drum switch contact pressure every three months

Last Answer : Answer: A

An old man wanted to leave all of his money to one of his three sons, but he didn't know which one he should give it to. He gave each of them a few coins and told them to buy something that would be able to fill their living room. The first man bought straw, but there was not enough to fill the room. The second bought some sticks, but they still did not fill the room. The third man bought two things that filled the room, so he obtained his father's fortune. What were the two things that the man bought? -Riddles

Description : An old man wanted to leave all of his money to one of his three sons, but he didn't know which one he should give it to. He gave each of them a few coins and told them to buy something ... filled the room, so he obtained his father's fortune. What were the two things that the man bought? -Riddles

Last Answer : The wise son bought a candle and a box of matches. After lighting the candle, the light filled the entire room.

An old man wanted to leave all of his money to one of his three sons, but he didn't know which one he should give it to. He gave each of them a few coins and told them to buy something that would be able to fill their living room. The first man bought straw, but there was not enough to fill the room. The second bought some sticks, but they still did not fill the room. The third man bought two things that filled the room, so he obtained his father's fortune. What were the two things that the man bought? -Riddles

Description : An old man wanted to leave all of his money to one of his three sons, but he didn't know which one he should give it to. He gave each of them a few coins and told them to buy something ... filled the room, so he obtained his father's fortune. What were the two things that the man bought? -Riddles

Last Answer : The wise son bought a candle and a box of matches. After lighting the candle, the light filled the entire room.

An old man wanted to leave all of his money to one of his three sons, but he didn't know which one he should give it to. He gave each of them a few coins and told them to buy something that would be able to fill their living room. The first man bought straw, but there was not enough to fill the room. The second bought some sticks, but they still did not fill the room. The third man bought two things that filled the room, so he obtained his father's fortune. What were the two things that the man bought? -Riddles

Description : An old man wanted to leave all of his money to one of his three sons, but he didn't know which one he should give it to. He gave each of them a few coins and told them to buy something ... filled the room, so he obtained his father's fortune. What were the two things that the man bought? -Riddles

Last Answer : The wise son bought a candle and a box of matches. After lighting the candle, the light filled the entire room.

A woman is put in a cement room without windows. The door is mechanically bolted shut and under strict watch so that nobody can come in or out. It is secured in every possible way. 24 hours later, the door is opened, and there are now 2 people inside the room. How is this possible? -Riddles

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Last Answer : The woman was pregnant.

I am passed from person to person but no hands are needed. I often change in this exchange. Always changing never remaining the same. What am l? -Riddles

Description : I am passed from person to person but no hands are needed. I often change in this exchange. Always changing never remaining the same. What am l? -Riddles

Last Answer : A rumour.

Every year, sometimes during winter and sometimes in the springtime, an elderly woman takes 12 pieces of food, each in its own separate colorful container, and strategically places them outside in her front and back yards. The woman then challenges select relatives to go retrieve the 12 pieces of food for her, so she can put them back into her refrigerator to be eaten later. When these select relatives ask her how the 12 pieces of food ended up outside in her yards, the elderly woman totally denies having put them there. Instead, ----- she blames an animal for the entire affair! Is this woman slip-sliding away mentally, or is there some method to her madness ----- and what animal does she blame? -Riddles

Description : Every year, sometimes during winter and sometimes in the springtime, an elderly woman takes 12 pieces of food, each in its own separate colorful container, and strategically places them outside in her front and ... is there some method to her madness ----- and what animal does she blame? -Riddles

Last Answer : The elderly woman has many grandchildren who she invites to her house each year to her annual Easter egg hunt! She challenges them to find the 12 colorful eggs the Easter Bunny has hidden for them.

What is the probability that the first two flips will both be heads and the third flip will be tails if you flip three fair coins?

Description : What is the probability that the first two flips will both be heads and the third flip will be tails if you flip three fair coins?

Last Answer : Need answer

A man has 3 wife's, each one has 3 houses, in one of houses for every wife his mother in law lives. He goes to first house with money, mother doubles it, he leaves half, he goes to second wife, mother doubles it again, he leaves the same amount as to first wife, he goes to third house and mother doubles it again, he leaves the same amount as to first one,but goes home with no money. How much money did he have? 2 wife are sister and they have a same mother? -Riddles

Description : A man has 3 wife's, each one has 3 houses, in one of houses for every wife his mother in law lives. He goes to first house with money, mother doubles it, he leaves half, he goes to second wife, ... with no money. How much money did he have? 2 wife are sister and they have a same mother? -Riddles

Last Answer : This answer was deleted by moderators

Who amongst the following has become the Chief Minister of a State in India third time consecutively? (1) Tarun Gogoi (2) Nitish Kumar (3) J. Jayalalithaa (4) None of these

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Last Answer : (1) Tarun Gogoi Explanation: Tarun Gogoi has become the Chief Minister of Assam for third consecutive term.

Is the filament resistance lower or higher in a 500 watt light bulb than in a 100 watt light? Assume that both bulbs have been designed to operate at 110 volts.

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Last Answer : ANSWER: LOWER

One day, you woke up in a place you havent seen before. There, you saw three rooms, all bring you to the exit. But, on those rooms, there were notes. It said: 1: room is filled with poison gas 2: room has more than 15 lions that havent eaten for 5 years 3: room is fiiled with snipers that would kill anyone who steps in You have no other choice, but to choose one of the three. Which room would be the way that could get you out without being harmed? -Riddles

Description : One day, you woke up in a place you havent seen before. There, you saw three rooms, all bring you to the exit. But, on those rooms, there were notes. It said: 1: room is filled with poison ... choose one of the three. Which room would be the way that could get you out without being harmed? -Riddles

Last Answer : 2. Because if the lions hadn't eaten for five years, they would be dead.

There is an island with exactly 201 residents, 100 with blue eyes, 100 with brown eyes, and the island leader (who has green eyes). To leave the island, one must know their own eye color. There are no reflective surfaces on the island and no on can communicate with each other other than the leader to the residents. No one on the island knows how many of each eye color there is. Everyone on the island is a perfect logician, meaning that if there is a solution they'll find it. Every morning the leader gives anyone a chance to leave the island by guessing their eye color. One morning, the leader gathers all 200 residents to make an announcement, he says 'at least 1 person on this island has blue eyes' How many people leave the island and in how many days after the announcement? Notes: this is

Description : There is an island with exactly 201 residents, 100 with blue eyes, 100 with brown eyes, and the island leader (who has green eyes). To leave the island, one must know their own eye color. There ... How many people leave the island and in how many days after the announcement? Notes: this is -Riddles

Last Answer : All 100 blue eyed people in 100 days. EXPLANATION: imagine there is only 1 person on the island, he will look around and see that there are no blue eyed people, he will then know his eye color in ... is needed to know their own eye color. if you would like more info, search '100 blue eyes riddle

My first is often at the front door. My second is found in the cereal family. My third is what most people want. My whole is one of the United States. -Riddles

Description : My first is often at the front door. My second is found in the cereal family. My third is what most people want. My whole is one of the United States. -Riddles

Last Answer : Matrimoney. (mat + rye + money). Matrimony is certainly a 'united state'!

My first is often at the front door. My second is found in the cereal family. My third is what most people want. My whole is one of the United States. What am I? -Riddles

Description : My first is often at the front door. My second is found in the cereal family. My third is what most people want. My whole is one of the United States. What am I? -Riddles

Last Answer : MATRIMONY (mat rye money). Which is certainly a 'united state'!

I have many keys, but no lock. I have space, but no room. I can enter, but I can't exit. What am I? -Riddles

Description : I have many keys, but no lock. I have space, but no room. I can enter, but I can't exit. What am I? -Riddles

Last Answer : A keyboard.

Old Mr. Tilly was found dead in his study by Mr. Foster. Mr. Foster recounted his dismal discovery to the police. 'I was walking by Mr. Tilly`s house when I thought I would just pop in for a visit. I noticed his study light was on and I decided to peek in from the outside to see if he was in there. There was frost on the window, so I had to wipe it away to see inside. That is when I saw his body. So I kicked in the front door to confirm my suspicions of foul play. I called the police immediately afterward.' The officer immediately arrested Mr. Foster for the murder of Mr. Tilly. How did he know Mr. Foster was lying? -Riddles

Description : Old Mr. Tilly was found dead in his study by Mr. Foster. Mr. Foster recounted his dismal discovery to the police. 'I was walking by Mr. Tilly`s house when I thought I would just pop in for a ... arrested Mr. Foster for the murder of Mr. Tilly. How did he know Mr. Foster was lying? -Riddles

Last Answer : Frost forms on the inside of the window, not the outside. So Mr. Foster could not have wiped it off to discover Mr. Tilly`s body.

What word can be grammatically correct, when used consecutively in the English language? -Riddles

Description : What word can be grammatically correct, when used consecutively in the English language? -Riddles

Last Answer : Had:''James while John had had had had had had had had had had had a better effect on the teacher' is an English sentence used to demonstrate lexical ambiguity and the necessity of punctuation, ... as a substitute for the intonation, stress, and pauses found in speech.'-Wikipedia. Cool, Huh?

There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it? -Riddles

Description : There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it? -Riddles

Last Answer : Place the apple on one person's head.

A set of 121 chairs needs to be arranged in a square formation for a school assembly. How many chairs should be lined up in each row?

Description : A set of 121 chairs needs to be arranged in a square formation for a school assembly. How many chairs should be lined up in each row?

Last Answer : 1

There was a penny that had 5 children. The first was named November. December was the second ones name. The third, January. February was the fourth ones name. What was the final ones name. -Riddles

Description : There was a penny that had 5 children. The first was named November. December was the second ones name. The third, January. February was the fourth ones name. What was the final ones name. -Riddles

Last Answer : The fifth ones name is what.

Place three piles of matches on a table, one with 11 matches, the second with 7, and the third with 6. You are to move matches so that each pile holds 8 matches. You may add to any pile only as many matches as it already contains. All the matches must come from one other pile. For example, if a pile holds 6 matches, you may add 6 to it, no more or less. You have three moves. -Riddles

Description : Place three piles of matches on a table, one with 11 matches, the second with 7, and the third with 6. You are to move matches so that each pile holds 8 matches. You may add to any pile only as many ... a pile holds 6 matches, you may add 6 to it, no more or less. You have three moves. -Riddles

Last Answer : First pile to second; second to third; third to first:Pile Initial number First move Second move Third move First1111-7=444+4=8Second77+7=1414-6=88Third666+6=1212-4=8