Riddle: What number squared = 12345678987654321?
Riddle: A soccer fan, upset by the defeat of his favorite team, slept restlessly. In his dream a goalkeeper was practicing in a large unfurnished room, tossing a soccer ball against the wall and then catching it. But the goalkeeper grew smaller and smaller and then changed into a ping-pong ball while the soccer ball was swelled up into a huge cast-iron ball. The iron ball circled round madly, trying to crush the ping-pong ball, how did the ping-pong find safety whithout leaving the floor?
Answer: If the ping-pong ball rolls flush against the wall, the cast-iron ball cannot crush it. Those who know geometry can determine that if the diameter of a large ball is at least 5.83 (3+2(square root of 2) times as large as the diameter of a little ball, then the little ball will be safe if it hugs the wall. A cast-iron ball that is larger than a soccer ball is more than 4.83 times as large in diameter as a ping-pong ball.
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. What is 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.
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.
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.
Riddle: You go to the doctor because you're ill and he prescribes you with 3 pills and tells you to take them every half hour. How long do the pills last you?
Answer: An hour because the first pill doesn't take 30 min. to take.
Riddle: 0,1,2,3,4,5,6,7,8,9 How can you use the digits above once each only to compose two fractions which when added together equal 1?
Answer: 35/70 + 148/296 = 1
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.
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.
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.