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?
Think about the factors of each bulb number...
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.
You walk up to a mountain that has two paths. One leads to the other side of the mountain, and the other will get you lost forever. Two twins know the path that leads to the other side. You can ask them only one question. Except! One lies and one tells the truth, and you don't know which is which. So, What do you ask?
What weighs more, a pound of feathers or a pound of stones?
A logician with some time to kill in a small town decided to get a haircut. The town had only two barbers, each with his own shop. The logician glanced into one shop and saw that it was extremely untidy. The barber needed a shave, his clothes were unkempt, and his hair was badly cut. The other shop was extremely neat. The barber was freshly shaved and spotlessly dressed, his hair neatly trimmed. Why did the logician return to the first shop for his haircut?
George, Helen, and Steve are drinking coffee. Bert, Karen, and Dave are drinking soda. Using logic, is Elizabeth drinking coffee or soda?
Little Tommy Tittletat took two Ts, to tie two ups to two tall trees, to torment the terrible little tat. How many T's in all of that?
A man went on a trip with a fox, a goose, and a sack of corn. He came upon a stream that he had to cross and found a tiny boat to use to cross the stream. He could only take himself and one other - the fox, the goose, or the corn - one at a time. He could not leave the fox alone with the goose or the goose with the corn. How does he get all safely over the stream?
81 x 9 = 801. What must you do to make the this equation true?
One of the four words does not belong with the other three. Which word does not belong? What is it that the others have in common? 1. Green, yellow, red, blue. 2. April, December, November, June. 3. Cirrus, calculus, cumulus, stratus. 4. Carrots, radishes, potatoes, cabbages. 5. Fork, comb, rake, shovel.
If you have two coins which total 35 cents and one of the coins is not a dime, what are the two coins?
Open me, and you can't see me without a mirror. Close me and you can't see me at all. What am I?
I am a 5-letter word. Take away the first letter and I am a place's name. Take away the first two letters and I become the opposite of the 5 letter word. What am I?
You buy me taken apart, To redo what has been undone; Four of my pieces have one sharp corner, The rest of them have none. What am I?
What only works the first time you use it?
Which side of the turkey has the most feathers?
It's raining, and you pass a bus stop. There are three people there; your trustworthy friend, the love of your life, and a woman about to go into labor. Your smart car only has two seats. What do you do?
What's the least number of chairs you would need around a table to sit four fathers, two grandfathers, and four sons?
What's 3/7 chicken, 2/3 cat, and 2/4 goat?
I can hold you prisoner Or set you free I can swing with ease (Though not from a tree) I have many shapes I have many sizes Yet, 'til we shake hands I'll hide my surprises. What am I?
Many years ago, a wealthy old man was near death. He wished to leave his fortune to one of his three children. The old man wanted to know that his fortune would be in wise hands. He stipulated that his estate would be left to the child who would sing him half as many songs as days that he had left to live. The eldest son said he couldn't comply because he didn't know how many days his father had left to live, and besides he was too busy. The youngest son said the same thing. The man ended up leaving his money to his third child, a daughter. What did his daughter do?
If you see me, I see you. If you move, then I'll move too. When you touch me, I touch you. I do everything you do except for one thing. No matter how hard I try, I can never speak. What am I?