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Riddle:

Draw four rectangles on a piece of paper. Put nine x's in the four rectangles so that there is an uneven number of x's in each rectangle.

Answer:

Draw one large rectangle. Then draw the three smaller rectangles within the large rectangle. Place three x's in each small rectangle. There will be nine x's in the large rectangle.

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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.

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Riddle:

A hunter met two shepherds, one of whom had three loaves and the other, five loaves. All the loaves were the same size. The three men agreed to share the eight loaves equally between them. After they had eaten, the hunter gave the shepherds eight bronze coins as payment for his meal. How should the two shepherds fairly divide this money?

Answer:

The shepherd who had three loaves should get one coin and the shepherd who had five loaves should get seven coins. If there were eight loaves and three men, each man ate two and two-thirds loaves. So the first shepherd gave the hunter one-third of a loaf and the second shepherd gave the hunter two and one-third loaves. The shepherd who gave one-third of a loaf should get one coin and the one who gave seven-thirds of a loaf should get seven coins.

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Riddle:

What number squared = 12345678987654321?

 

Answer:

111,111,111

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Riddle:

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?

 

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 down and up movesof the blue pencil smears 1 more inch of each pencil. 5 pairs of moves will smear 5 inches. This together with the initial inch, makes 6 inches for each pencil.

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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

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Riddle:

The title of the problem tells you how to approach these four questions.

(A).  A bus leaves Moscow for Tula at noon. An hour later a cyclist leaves Tula for mosco, moving slower than the bus. When the bus and cyclist meet, which one of the two will be farther from Moscow?

(B). Which is worth more: a pound of $10 gold peices or half a pound of $20 gold pieces?

(C). At six o'clock the wall clock struck 6 times. Checking with my watch, I noticed the time between the first and last strokes was 30 seconds. How long will the clock take to strike 12 at midnight?

(D). Three swallows fly outward from a point. When will they all be on the same plane in space?

Now check the answers. Did you fall into any of the traps which lurk in these simple problems?

Answer:

(A). Neither

(B). A pound of metal is always more than half a pound of the same metal.

(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.

(D). There is always a plane that contains any 3 points 

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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. 

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Riddle:

An alarm clock runs 4 minutes slow every hour. It was set right 3 1/2 hours ago. Now another clock which is correct shows noon. 

In how many minutes, to the nearest minutes, to the nearest minute, will the alarm clock show noon?

Answer:

In 3 1/2 hours the alarm clock has become 14 minutes slow. At noon the alarm clock will fall behind approximently an additional minute. Its hands will show noon in 15 minutes.

 

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Riddle:

You have accidently left out the plug and are attempting to fill the bath with both taps full on. The hot tap takes 6 minutes to fill the bath. The cold tap takes 2 minutes and the water empties through the plug hole in 4 minutes.

In how many minutes will the bath be filled?

Answer:

2 minutes and 24 seconds.

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