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Puzzles - 4
1. Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet. How far does the pigeon travel?

2. Nick and John were exercising when the subject of weight came up. Nick had no problem telling John his weight, but John said he had more "mass" than he wanted. He wouldn't come right out and reveal his weight; so he told Nick this riddle. " I weigh 147 pounds plus half of my weight," he said. How much does he weigh?

3. A farmer knows that 20 of his hens, housed in 3 coops, will hatch 30 eggs in 18 days. How long will it take 30 hens, housed in 4 coops to hatch the same number of eggs?

4. How can you measure 1 gallon of juice out of a barrel, if all you have available is a 3-gallon and a 5-gallon pitcher?

5. Students at Monty High with a class size under of 30 took a math test. One third of the class got a "B", one quarter a "B-", one sixth a "C", and one eighth failed. The remainder of the students got an "A" How many students got an "A"?

6. When manufacturing bars of soap, the cutting machine produces scraps. The scraps from 11 bars of soap can be made into one extra bar. What is the total number of bars that can be made after cutting 250 bars of soap?

7. Kerry loves dumplings. He can eat 32 of them in an hour. His brother Pete needs 3 hours to eat the same amount. How long will it take them both together to eat 32 dumplings?

8. Joan and Jane are sisters. Jean is Joan's daughter and 12 years younger than her aunt. Joan is twice as old as Jean. Four years ago, Joan was the same age as Jane is now, and Jane was twice as old as her niece. How old is Jean?

9. Find a simple method of solving:
6751X + 3249Y = 26751
3249X + 6751Y = 23249

10. Divide 110 into two parts so that one will be 150 percent of the other. What are the 2 numbers?

11. At a sports banquet there are one hundred athletes. Each one is either a football or basketball player. At least one is a football player. Given any two of the athletes, at least one is a basketball player. How many of the athletes are football players?

12. The following number is the only one of its kind. Can you figure out what is so special about it? 8,549,176,320

13. Jennifer took a test that had 20 questions. The total grade was computed by awarding 10 points for each correct answer and deducting 5 points for each incorrect answer. Jennifer answered all 20 questions and received a score of 125. How many wrong answers did she have?

14. A box of candy bars can be divided equally (without cutting anything) among 2, 3, or 7 people. What is the least number of candy bars the box could contain?

15. Using standard mathematical symbols, e.g. +, -, x, etc., rearrange (4) fives to equal the numbers one to ten. For example, 5/5 + 5 - 5 = 1, 5/5 + 5/5 = 2, etc.

16. Use each of the digits 1, 2, 3, 4, 5 and 6 once only, in this multiplication problem to make it correct.

? ?
x ?
? ? ?

17. Bob is ten years older than his brother Stan. There was a time when Bob was three times as old as Stan. What was Stan's age when Bob was three times as old?

18. Can you replace the question marks with three math symbols to make the following equation correct:
(2 ? 3) ? (6 ? 2) ? (3 ? 1) = 5

19. Can you find four consecutive prime numbers that add up to 220?

20. If I buy an apple and a banana, the cost will be $1.19. If I buy an apple and a pear, the cost will be $1.45. If I buy a banana and a pear, the cost will be $1.40. What are the individual prices?

21. A two-digit number when read from left to right, is 4.5 times less than the same number read from right to left. What is the number?

22. Barry went to a sporting goods store with $100 to buy some golf equipment. If he spent $40 on a new driver, 20% of what was left on a new putter, 1/8 of his original money on golf balls, and 31/71 of what was left of his money on a golf cart, how much money does he have left?

23. If 3 salesman can sell three stoves in 7 minutes, how many stoves can six salesmen sell in seventy minutes?

24. You have a cake which you must cut into 8 equal pieces. You may make only 3 cuts. How will do this?

25. Which number when added to 5/4 gives the same result as when it is multiplied 5/4?

26. In the square below, a rule applies both from top to bottom and from left to right. Find the rule and figure out the missing number.
6 2 4
2 ? 0
4 0 4

27. What is the missing number in this arrangement?
1 2 3 4 5
1 3 7 15 31
1 4 13 40 121
1 5 21 85 ???

28. A fish is fifteen inches long. Its head is as long as its tail. If the head were twice as long as it really is, the head and tail would together be as long as what's in between. How long is each part of the fish?

29. Arrange the ten digits 0 to 9 in three arithmetical sums, using three of the four operations of addition, subtraction, multiplication, and division, and using no signs except the ordinary ones implying those operations. Here is an example to make it quite clear (note that the example is not correct):
3 + 4 = 7 9 - 8 = 1 5 X 6 = 30

30. Several cartons of candy are being shipped from a manufacturer to warehouses where they will be prepackaged to sell to stores. The candy in each carton needs to be divided equally among 3, 4, 5, or 7 stores. What is the least number of pieces of candy that each carton can have?

31. Kevin flew to Puzzle land at the fantastic speed of 1000 miles per hour. There he picked up his friend and flew back, burdened by the extra weight, at only 500 miles per hour. What was his average speed?

32. What is the number that is 5 more than the number which is one-fifth of one-fifth of one-half of 1050?

33. The following multiplication example uses every digit from 0 to 9 once (not counting the intermediate steps). Fill in the missing numbers.
7 x x
4 x
x x x x x

34. There are 7 tennis balls which are identical in all aspects except that one of them weighs slightly less than the other 6. How can you identify the one that weighs less on a balance scale with no more than 2 separate weighings?

35. Fill in the missing numbers in the following series:
101 99 102 98 103 97 ? ?

36. Can you arrange the odd digits 1, 3, 5, 7, and 9, and the even digits, 2, 4, 6, and 8, in such a way that the odd ones add up to the same as the even ones? You can use arithmetical signs and decimals, but the idea is to try and arrive at the simplest possible solution. There are, of course, many possible answers.

37. Many years ago when gasoline was only 46 cents a gallon, I stopped to fill up my car. I gave the attendant a $20.00 bill and waited for my change. Unexpectedly, he charged me for the number of gallons that the car needed instead of the dollar amount. (for example if the car took 8.4 gallons he would have charged me $8.40. Because he did this, I received less in change than I should have. The funny thing is that I had received in change exactly the amount that I should have been charged for the gas in the first place. Remembering that the cash indicator on a gas pump will only charge to the nearest half-cent, how many gallons of gas did I buy that day?

38. What is the four-digit number (no zeros) in which the third digit is the number of "winds," the first digit is one-half of the third, the second digit is double the third and the last digit is one-half the sum of the first three?

39. What would be the next number in the following sequence?
11 1,331 161,051 19,487,171 ?

40. The square of 13 is 169. Take the last digit of the square, 9, and place it in the middle, making 196. This is the square of 14, the next number above 13. What are the next numbers which also have this property?

41. The following multiplication example uses every digit from 0 to 9 at least once. Letters have been substituted for the digits. Can you replace the letters and make the original multiplication problem?
x B O G

42. There are several ways to come up with 100 by using the digits 0 through 9. One way is: 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 x 9) = 100. Another way is 78 3/6 + 21 45/90. Can you come up with 2 more ways?

43. If 1/2 of 16 were 13, what would 1/3 of 32 be?

44. Sheilah is now two-thirds of Sally's age. In six years, Sheilah will be four-fifths of Sally's age. In 15 years, Sheilah will be seven-eighths as old as sister Sally. If they are both under the age of ten, how old are they now?

45. You have a huge box of beautiful decorated tiles, enough to provide a border in two rooms. You really can't figure out how to arrange them, however. If you set a border of two tiles all around, there's one left over; if you set three tiles all around, or four, or five, or six, there's still one tile left over. Finally; you try a block of seven tiles for each corner, and you come out even. What is the smallest number of tiles you could have to get this result?

46. A car company sold 150 cars in a special 6-day tent sale offer. Each day the company sold 6 more cars than the day before. How many cars were sold on the 6th day?

47. When the two met, one was half the other's age plus seven years. Ten years later, when they married, the bride was thirty, but this time one was nine-tenths the age of the other. How old was the groom? ( no fractions, no partial years---whole numbers only.)

48. Mona and Allen went shopping for groceries. They spent half of what they had plus $2.00 at the butcher shop. At the dairy, they spent half of what was left, plus $5.00. At the bakery, they spent half of what was left. The remaining $5.00 was spent on coffee and cake. How much did they start with?

49. Take the number of your fingers (10) multiplied by the number of you toes (10) divided by one half and add it to the number of months in a year. What is the total?

50. A mother and father have six sons and each son has one sister. How many people are in that family?

51. Jenn has half the Beanie Babies that Mollie has. Allison has 3 times as many as Jenn. Together they have 72. How many Beanie Babies does each girl have?

52. Kevin is 14 inches taller than George. The difference between Kevin and Richard is two inches less than between Richard and George. Kevin at 6'6" is the tallest. How tall are Richard and George?

53. A baseball team had just won the championship game and the players wanted to congratulate each other. They began shaking hands, but each player only shook hands with every other player just once. There are, of course, only 9 players on a baseball team. How many times did the players shake hands?

54. A jar has 4 amoebas in it to start. Amoebas split their cells in two ( therefore doubling in size) once every minute. The jar will be completely filled in 10 minutes. How long would it take to fill the same sized jar if had 8 amoebas in it to start?

55. There are 100 golfers in the local match play contest. If a player loses a match, he is immediately eliminated from the contest. How many matches will be played to determine the winner?

56. Two trains are on a head on collision course. The trains are currently 65 miles apart. The north bound train is traveling at 55 miles per hour and the south bound train is traveling at 80 miles per hour. What is the distance between the trains two minutes before they collide?

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