1. Haretown and Tortoiseville are 63 miles apart. A hare travels at 8 miles per hour from Haretown to Tortoiseville, while a tortoise travels at 1 miles per hour from Tortoiseville to Haretown.

If both set out at the same time, how many miles will the hare have to travel before meeting the tortoise en route?

2. Man Wrinkle spent one-fourth of his life as a boy, one-eighth as a youth, and one-half as an active man. If Man Wrinkle spent 8 years as an old man, then how many years did he spend as an active man?

3. Dad gives you money every day to put in your new piggy bank. He gives money to you in such a way that the money in the piggy bank doubles with each passing day.

If you already have 1 cent in the piggy bank and Dad gives you 1 cent the first day, 2 cents the second day, 4 cents the third day and so on, then your piggy bank gets full on the 10th day.

1. On which day will your piggy bank be half-full? For example, type 6 if your answer is 6th day.

2. In addition to Dad's contributions, if Mom also gave you 1 cent the first day, 2 cents

the second day, 4 cents the third day and so on, then on which day would your piggy

bank be about half-full? For example, type 6 if your answer is 6th day.

4. Rectangles on Checkered Board

If you were to construct a 5 × 5 checkered square (i.e., a 5 × 5 chess board), how many rectangles would there be in total? You need to include squares too because a square is a special kind of rectangle.

5. A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 2 hours to fill the tank with the large inlet pipe. On the other hand, it takes 4 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be

emptied in 6 hours.

What fraction of the tank (initially empty) will be filled in 1.71 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).

6. My Dad has a miniature Pyramid of Egypt. It is 5 inches in height. Dad was invited to display it at an exhibition. Dad felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1 / 5) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough.

If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid? Give your answer to two places of decimal.

7. A creeper plant is climbing up and around a cylindrical tree trunk in a helical manner. The tree trunk has a height of 525 inches and a circumference of 40 inches.

If the creeper covers a vertical distance of 75 inches in one complete twist around the tree trunk, what is the total length of the creeper?

8. The 10" pizza sells for $ 5.99 at my favorite pizza store. The store claims they have a great deal on the large 14" pizza, which is specially priced at $ 9.98. What is the per cent discount the store is offering?

9. Grandpa:

"My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 100 years. Can you tell me my age in years?"

10. The son of a rich bullion merchant left home on the death of his father. All he had with him was a gold chain that consisted of 110 links. He rented a place in the city center with a shop at the lower level and an apartment at the upper level. He was required to pay every week one link of the gold chain as rent for the place.

The landlady told him that she wanted one link of the gold chain at the end of one week, two gold links at the end of two weeks, three gold links at the end of three weeks and so on.

The son realized that he had to cut the links of the gold chain to pay the weekly rent. If the son wished to rent the place for 110 weeks, what would be the minimum number of links he would need to cut?

11. The Rectangle at the Corner

In the above figure, the rectangle at the corner measures 8 cm x 16 cm. What is the radius of the circle in cm?

12. Divide $75 (in whole $ increments) into a number of bags so that I can ask for any amount between $1 and $75, and you can give me the proper amount by giving me a certain number of these bags without opening them. What is the minimum number of bags you will require?

13. The String on the Cylinder

A cylinder 72 cm high has a circumference of 16 cm. A string makes exactly 6 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?

14. If the difference of two numbers is 9 and their product is 19, what is the sum of their squares?

15. The Pole in the Lake

There is a pole in a lake. One-half of the pole is in the ground, another one-third of it is covered by water, and 8 ft is out of the water. What is the total length of the pole in ft?

16. If you were to construct a 6 x 6 checkered square (i.e., a 6 x 6 chess board), how many squares would there be in total?

17. In a Circle

A number of children are standing in a circle. They are evenly spaced and the 7th child is directly opposite the 19th child. How many children are there altogether?

18. Each child in a family has at least 3 brothers and 2 sisters. What is the smallest number of children the family might have?

19. Glenn and Jason each have a collection of tennis balls. Glenn said that if Jason would give him 6 of his balls they would have an equal number; but, if Glenn would give Jason 6 of his balls, Jason would have 3 times as many balls as Glenn. How many balls does Jason have?

20. Freddie takes the underground train to work and uses an escalator at the railway station. If Freddie runs up 7 steps of the escalator, then it takes him 40.5 seconds to reach the top of the escalator. If he runs up 15 steps of the escalator, then it takes him only 28.5 seconds to reach the top.

How many seconds would it take Freddie to reach the top if he did not run up any steps of the escalator at all?

21. It was vacation time, and so I decided to visit my cousin's home. What a grand time we had! In the mornings, we both would go for a jog. The evenings were spent on the tennis court. Tiring as these activities were, we could manage only one per day, i.e., either we went for a jog or played tennis each day. There were days when we felt lazy and stayed home all day long.

Now, there were 9 mornings when we did nothing, 14 evenings when we stayed at home, and a total of 11 days when we jogged or played tennis. For how many days did I stay at my cousin's place?

22. Bodo weighs 120 pounds more than his sister Cheryl. Their combined weight is 160 pounds. How many pounds does Bodo weigh?

23. A set of football matches is to be organized in a "round-robin" fashion, i.e., every participating team plays a match against every other team once and only once.

If 55 matches are totally played, how many teams participated?

24. A snake slides through a long cylindrical hole in the ground at 4 centimeters per second. The hole is 5.36 meters in length. The snake takes 15 seconds to enter the hole.

1. What is the length in centimeters of the snake ?

2. How many seconds does the snake take to exit the hole after entering it?

25. A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, "How many gold coins do we have?"

After pausing a moment, he replied, "Well! If I divide the coins into two unequal numbers, then 68 times the difference between the two numbers equals the difference between the squares of the two numbers."

The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins they have?

26. Bill: "When I add 3 times my age 3 years from now to 4 times my age 4 years from now, I get 8 times my current age. How old will I be 5 years from now?"

A). A tennis championship is played on a knock-out basis, i.e., a player is out of the tournament when he loses a match.

1. How many players participate in the tournament if 63 matches are totally played?2. How many matches are played in the tournament if 120 players totally participate?

27. The drive from Oakland to Pinewood was a tricky one. I covered the uphill distance of 55 miles at 35 miles per hour. The return journey from Pinewood to Oakland was downhill, and I managed to drive at 63 miles per hour. What was my average speed for the entire journey?

28. There is a number that is 3 times the sum of its digits. What is this number?

29. "Dad, where had you been?" asked Graham.

"I had been to the attic, my son," replied Dad. "And do you know what I saw there? There was a big web with 18 spiders and flies on it."

"How many spiders were there?" asked the little boy with curiosity.

"Well, there were a total of 120 legs on the web," answered Dad with a smile. "Now you can find out how many spiders were there by yourself. Can't you?"

Can you help the little boy find out how many spiders were on the web in the attic?

30. A block of wood in the form of a cuboid 3" × 9" × 11" has all its six faces painted pink. If the wooden block is cut into 297 cubes of 1" × 1" × 1", how many of these would have pink paint on them?

31. The distance between Station Atena and Station Barcena is 78 miles. A train starts from Atena towards Barcena. A bird starts at the same time from Barcena straight towards the moving train. On reaching the train, it instantaneously turns back and returns to Barcena. The bird makes these journeys from Barcena to the train and back to Barcena continuously till the train reaches Barcena. The bird finally returns to Barcena and rests. Calculate the total distance in miles the bird travels in the following two cases:

1. the bird flies at 70 miles per hour and the speed of the train is 60 miles per hour

2. the bird flies at 60 miles per hour and the speed of the train is 70 miles per hour

32. Last vacation, my cousin came over to stay at my home. We made the most of her stay at my place... and I even earned a few chocolates.

Everyday, we would play a game of chess. Whoever lost the game owed a chocolate to the other. After the last game we played (that was the day she was to leave), we counted the number of games each of us had won and lost. Wow! I had won more than her. So, she handed me 16 chocolates... though she herself was the winner in 7 games.

How many days did my cousin spend at my place?

33. It was Linda's first day at school. The teacher suggested that it would be a good idea for each child to meet every other child in the class. The teacher said, "When you meet, please shake hands and introduce yourself by name."

If there were 7 children in the class, how many total handshakes were there?

34. A painting job can be completed by 6 painters in 17 days. If 12 more painters join the team 5 days after starting work on the job, then how many more days are required to complete the job?

35. A snail creeps 4 ft up a wall during the daytime. After all the labor it does throughout the day, it stops to rest a while... but falls asleep!! The next morning it wakes up and discovers that it has slipped down 1 ft while sleeping.

If this happens every day, how many days will the snail take to reach the top of a wall 10 ft in height?

36. Your teacher has a total of 49 chalks. When a chalk reduces to 1/7 of its original size, it gets too small for her to hold for writing and hence she keeps it aside. But your teacher hates wasting things and so, when she realizes that she has enough of these small pieces to join and make another chalk of the same size, she joins them and uses the new chalkstick. If she uses one chalk each day, how many days would the 49 chalks last?

37. A pillar 4 feet tall casts a shadow 2 feet long on the ground. If the pillar was 14 feet tall, how many feet in length would the shadow be ?

38. A 32" x 32" square metal plate needs to be fixed by a carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 33 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use?

39. Suppose 7 monkeys take 7 minutes to eat 7 bananas.

1. How many minutes would it take 4 monkeys to eat 4 bananas?

2. How many monkeys would it take to eat 63 bananas in 63 minutes?