Riddle:
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?
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.
Riddle:
You can use me to stop,
You take me to smoke;
Not only do I stop, But I am a stop,
And the result of pool's first stroke.
What am I?
Answer: Brake/ Break
Riddle:
Rearrange all the letters in each of the sentences to form, in each case, a well-known proverb.
1. I don't admit women are faint.
2. It rocks. The broad flag of the free.
3. Strong lion's share almost gone.
What are the proverbs?
Answer: 1. Time and tide wait for no man.
2. Birds of a feather flock together.
3. A rolling sone gathers no moss.
Riddle:
I am a perching barrel, filled with meat, Taking hits from leaps and dives. Look inside, but do not eat, The meat in there is still alive! What am I?
Answer: A thimble on a finger.
Riddle:
A great banquet was prepared for a Roman emperor and his courtiers. 22 Dormice, 40 Larks' Tongues, 30 Flamingos and 40 Roast Parrots were served.
How many portions of Boiled Ostrich were served?
Answer: 42. Each vowel is worth 2 and each consonant 4, so Dormice gives 22, ect.
Riddle:
You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weigh the same or that the dish that falls lower has heavier contents than the other. The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more. Note that the unusual marble may be heavier or lighter than the others. How can you identify it and determine whether it is heavy or light?
Answer: Number the marbles from 1 to 12. For the first weighing put marbles 1,2,3 and 4 on one side and marbles 5,6,7 and 8 on the other. The marbles will either they balance or not. If they balance, then the different marble is in group 9,10,11,12. Thus, we would put 1 and 2 on one side and 9 and 10 on the other. If these balance then the different marble is either 11 or 12. Weigh marble 1 against 11. If they balance, the different marble is number 12. If they do not balance, then 11 is the different marble. If 1 and 2 vs 9 and 10 do not balance, then the different marble is either 9 or 10. Again, weigh 1 against 9. If they balance, the different marble is number 10, otherwise, it is number 9. That was the easy part. What if the first weighing 1,2,3,4 vs 5,6,7,8 does not balance? Then any one of these marbles could be a different marble. Now, in order to proceed, keep track of which side is heavy for each of the following weighings. Suppose that 5,6,7 and 8 is the heavy side. We now weigh 1,5 and 6 against 2,7 and 8. If they balance, then the different marble is either 3 or 4. Weigh 4 against 9, a known good marble. If they balance then the different marble is 3 or 4. Then, if 1,5 and 6 vs 2,7 and 8 do not balance, and 2,7,8 is the heavy side, then either 7 or 8 is a different, heavy marble, or 1 is a different, light marble. For the third weighing, weigh 7 against 8. Whichever side is heavy is the different marble. If they balance, then 1 is the different marble. Should the weighing of 1,5 and 6 vs 2,7 and 8 show 1,5,6 to be the heavy side, then either 5 or 6 is a different heavy marble or 2 is a light different marble. Weigh 5 against 6. The heavier one is the different marble. If they balance, then 2 is a different light marble.
Riddle:
The word FACETIOUSLY contains the six vowels, A-E-I-O-U and Y, in their alphabetical order. Can you find another English word that does the same?
Answer: The word is abstemiously. There may be others.
Riddle:
If it is 1,800 kilometers to America, 1,200 kilometers to Japan, 2,400 kilometers to New Zealand, and 1,400 kilometers to Brazil-
How far is Morocco?
Answer: The answer is 1,700 kilometers, as vowels in the countries' names are worth 300 kilometers and the consonats are worth 200 kilometers.
Riddle:
Marco and Bob have been the best friends ever since they were little kids. They are also very competitive. Throughout the years they have challenged each other to do both physical and mental challenges. And they completed the challenge. But one day Marco thought of something to challenge Bob to do - something he could start but never finish. The average man could do it and so could Mark and they were both the same sex and the same size. It is a physical challenge. Can you figure out what it was?
Answer: Marco challenged Bob to get a tan, but he couldn't...Bob is an albino.
Riddle:
You have two container, a 5 gallon and a 3 gallon container. How do you measure out 4 gallons?
Answer: Fill up the 3 gallon container and pour the 3 gallons into the 5 gallon container.Then, fill the 3 gallon container back up, and pour it into the 5 gallon container.The 3 gallon container will have 1 gallon left. Empty the 5 gallon container.Pour the remining 1 gallon into the 5 gallon container.Then fill the 3 gallon container back up and pour it into the 5 gallon container.Thus, you have 4 gallons.
Riddle:
Hickory-Dickory-Dock! The mouse ran up the clock. The clock struck one and down did come. Hickory-Dickory-Dock!
What am I?
Answer: A guillotine.
Riddle:
It's always 1 to 6, it's always 15 to 20, it's always 5, but it's never 21, unless it's flying.
What is it?
Answer: The answer is: a dice. An explanation: "It's always 1 to 6": the numbers on the faces of the dice, "it's always 15 to 20": the sum of the exposed faces when the dice comes to rest after being thrown, "it's always 5": the number of exposed faces when the dice is at rest, "but it's never 21": the sum of the exposed faces is never 21 when the dice is at rest, "unless it's flying": the sum of all exposed faces when the dice is flying is 21 (1 + 2 + 3 + 4 + 5 + 6).
Riddle:
A boy leaves home in the morning to go to school. At the moment he leaves the house he looks at the clock in the mirror. The clock has no number indication and for this reason, the boy makes a mistake in interpreting the time (mirror-image). Just assuming the clock must be out of order, the boy cycles to school, where he arrives after twenty minutes. At that moment the clock at school shows a time that is two and a half hours later than the time that the boy saw on the clock at home. What time is it?
Answer: The difference between the real time and the time of the mirror image is two hours and ten minutes (two and a half hours, minus the twenty minutes of cycling). Therefore, the original time on the clock at home that morning could only have been five minutes past seven: The difference between these clocks is exactly 2 hours and ten minutes (note that also five minutes past one can be mirrored in a similar way, but this is not in the morning!). Conclusion: The boy reaches school at five minutes past seven plus twenty minutes of cycling, which is twenty-five minutes past seven!...
Riddle:
Ben walked into a hardware store and asked the price of some items. The salesman said: One costs $1, Eight costs $1, Seventeen cost $2, One hundred four costs $3 and One thousand seventy two costs $4. What was Ben buying?
Answer: Ben was buying home address numbers and they cost $1 per digit.
Riddle:
An item is made from lead blanks in a lathe shop. Each blank suffices for 1 item. Lead shavings accumulated for making 6 items can be melted and made into a blank. How many items can be made from 36 blanks?
Answer: From 36 blanks there are 36 items made. The lead shavings are enough to make 6 blanks. Which make 6 more items. But don't stop here. The new shavings are good for 1 more item. Total: 43.
Riddle:
How can this be true? Have a look at the picture. All the lines are straight, the shapes that make up the top picture are the same as the ones in the bottom picture so where does the gap come from?
Answer: The green triangle has dimensions 2 x 5 and gradient 2 / 5 = 0.4 The red triangle has dimensions 3 x 8 and gradient 3 / 8 = 0.375 Hence the gradient of the green triangle is greater than that of the red triangle.
Riddle:
Carl is trying to find solutions to a geometric puzzle. He has a square plot of land that he needs to reserve 1/4 for himself and divide the remaining 3/4 equally and in a similar shape, among his 4 children. There are two possible solutions. Can you solve the puzzle?
Answer: Solution #1 - Squares
First, Carl divides his as to reserve to himself one-fourth in the form of a square.
Then, Carl takes the remaining 3/4 shape and scales it down by 1/4. He then, multiplies the shape into 4 identically shaped pieces, and aranges them so that they fit into the original 3/4 shape.
Solution #2 - Rectangles
First, create a triangle that is 1/4 the size of the square.
Now, with straight lines, create two squares.
Proceed to disect the two squares with horizontal lines creating 4 triangles.
Then, disect one of the resultuing triangles from each square. The shape of land for each of his four children is divided evenly and is the same shape.
Then, Carl takes the remaining 3/4 shape and scales it down by 1/4. He then, multiplies the shape into 4 identically shaped pieces, and aranges them so that they fit into the original 3/4 shape.
Solution #2 - Rectangles
First, create a triangle that is 1/4 the size of the square.
Now, with straight lines, create two squares.
Proceed to disect the two squares with horizontal lines creating 4 triangles.
Then, disect one of the resultuing triangles from each square. The shape of land for each of his four children is divided evenly and is the same shape.
Riddle:
Two travelers spend from 12 o'clock to 6 o'clock walking along a level road, up a hill, and back again. Their pace is 4 mph on the level, 3 mph uphill, and 6 mph downhill.
How far do they walk and at what time do they reach the top of the hill?
Answer: 24 miles half past three.
Riddle:
Robert and David were preparing to have a water balloon fight. "No Fair" cried Robert, "You have 3 times as many as I do!" David said "Fine!" and gave Robert 10 more balloons. "Still not fair!" argued Robert, "You still have twice as many as I do." How many more balloons must David give Robert for them to have the same number?
Answer: David must give Robert another 20 water balloons, giving them each 60. Robert started with 30 water balloons and David with 90.
Riddle:
What number, when added separately, to 100 and 164 can make each a perfect square?
Answer: The answer is 125. 125+100=225 and 125+164=289. The square root of 225 is 15 and the square root of 289 is 17.
