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Riddle:

How many cats are in a small room if in each of the four corners a cat is sitting, and opposite each cat there sit three cats, and a each cat's tail another is sitting?

Answer:

Four cats, each near a tail of a cat in an adjacent corner.

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Riddle:

When the celebrated German mathematician Karl Friedrich Gauss (1777-1855) was nine he was asked to add all the integers from 1 through 100. He quickly added 1 to 100, 2 to 99, and so on for 50 pairs of numbers each adding to 101.

Answer: 50 X 101=5,050.

Now find the sum of all the digits in integers from 1 through 1,000,000,000.

That's all the digits in all the numbers, not all the numbers themselves.

Answer:

The numbers can be grouped by pairs:

999,999,999 and 0;

999,999,998 and 1'

999,999,997 and 2;

and so on....

There are half a billion pairs, and the sum of the digits in each pair is 81. The digits in the unpaired number, 1,000,000,000, add to 1. Then:

(500,000,000 X 81) + 1= 40,500,000,001.

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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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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:

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:

A mother has three sick children. She has a 24-ounce bottle of medicine and needs to give each child eight ounces of the medicine. She is unable to get to the store and has only three clean containers, which measure 5, 11 and 13 ounces. The electricity is out and she has no way of heating water to wash the containers and doesn't want to spread germs. How can she divide the medicine to give each child an equal portion without having any two children drink from the same container?

Answer:

Fill the 5 oz. and 11 oz. Containers from the 24 oz. container. This leaves 8 oz. in the 24 oz. bottle. Next empty the 11 oz. bottle by pouring the contents into the 13 oz. bottle. Fill the 13 oz. bottle from the 5 oz. container (with 2 oz.) and put the remaining 3 oz. in the 11 oz. bottle. This leaves the 5 oz. container empty. Now pour 5 oz. from the 13 oz. bottle into the 5 oz. bottle leaving 8 oz. in the 13 oz. bottle. Finally pour the 5 oz. bottle contents into the 11 oz. bottle giving 8 oz. in this container.

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Riddle:

0,1,2,3,4,5,6,7,8,9

Use the digits above once each only to compose two fractions which when added togeather equal 1.

Answer:

35/70 + 148/296 = 1

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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 weight 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 a 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. You are asked to both identify it and determine whether it is heavy or light

Answer:

Most people seem to think that the thing to do is weight six coins against six coins, but if you think about it, this would yield you no information concerning the whereabouts of the only different coin. As we already know that one side will be heavier than the other. So that the following plan can be followed, let us number the coins from 1 to 12. For the first weighing let us put on the left pan coins 1,2,3,4 and on the right pan coins 5,6,7,8. There are two possibilities. Either they balance, or they don't. If they balance, then the different coin is in the group 9,10,11,12. So for our second weighing we would put 1,2 in the left pan and 9,10 on the right. If these balance then the different coin is either 11 or 12. Weigh coin 1 against 11. If they balance, the different coin is number 12. If they do not balance, then 11 is the different coin. If 1,2 vs 9,10 do not balance, then the different coin is either 9 or 10. Again, weigh 1 against 9. If they balance, the different coin 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 coins could be the different coin. Now, in order to proceed, we must keep track of which side is heavy for each of the following weighings. Suppose that 5,6,7,8 is the heavy side. We now weigh 1,5,6 against 2,7,8. If they balance, then the different coin is either 3 or 4. Weigh 4 against 9, a known good coin. If they balance then the different coin is 3, otherwise it is 4. Now, if 1,5,6 vs 2,7,8 does not balance, and 2,7,8 is the heavy side, then either 7 or 8 is a different, heavy coin, or 1 is a different, light coin. For the third weighing, weigh 7 against 8. Whichever side is heavy is the different coin. If they balance, then 1 is the different coin. Should the weighing of 1,5, 6 vs 2,7,8 show 1,5,6 to be the heavy side, then either 5 or 6 is a different heavy coin or 2 is a light different coin. Weigh 5 against 6. The heavier one is the different coin. If they balance, then 2 is a different light coin.

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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:

Jenna wrote all the numbers from 300 to 400 on a piece of paper. How many times did she write the digit 3?

Answer:

Jenna wrote it 120 times.

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