Math Magic: To Predict Unknown

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One of the math magic is to predict unknown facts. Please find below several situations where math gives unexpected and useful answers.

1. Code Testers

John detected 2 errors and Mary – 3 errors in a code. There is one error in common. How many errors are still undetected?

It looks like a joke. However there is a mathematical solution of the problem that shows that the number of undetected errors is N. I am sure that you can easily to find the number N.

99.9% fail or refuse to solve it.

 

2. Lake Width

 

How estimate the width of a lake without crossing it? You just walk and make some measures at a lakeside.

 

ImageFor example in the situation shown at the picture the width of the lake is 200 meters.

 

3. How many fish are there in the lake?

Yesterday, I caught 30 fish of a certain size in the lake.
I marked and released them without any harm.
Today I also caught and released 80 fish of the same size and noticed that there were 6 marked fish in the second catch.

How many fish of the same size are there in the lake?

4.  Seller’s decision

ImageI sell my car. People come to my garage one at a time and make bids to buy it. I make an immediate decision whether to accept or reject an offer after receiving it. I decide to reject the first N offers, mark the highest price P, and accept the first offer that is greater than P.

What number N do you recommend me if I expect that 100 people can make a bid?

If N is small, I can accept a small amount of money.
If N is large, I can reject the best offer.

This is the famous problem of the optimal stopping theory (Secretary Problem).

5. Winning Strategy

In a game, Anna and Bill take 1, 2, or 3 coins on each turn. The player to take the last coin from the pile wins. If Anna goes first and there are 40 coins on the table, how many coins should she take to guarantee that she would win?

The truth is “She always loses if Bill knows the winning strategy.” Do you know Bill’s strategy?

 

 

You Are A Math Genius!

Everybody was born a genius! You too!Young and Successful

Unleash the genius that sleeps within.

How? Make your brain work!

One of the possibilities is a small everyday dose of brain work.

Look at the puzzle below.

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At the beginning, it can drive you crazy.

Don’t give up!

Take an easier challenge and GROW!

Aplusclick provides you with an enormous opportunity for everyday training!

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You start with unpractical number puzzles and finish by solving practical optimization problems such as finding the shortest underground route …

… or packing the maximum possible number of boxes in a room.

Remember: You are a genius! Don’t miss an opportunity to grow!

A rendezvous at www.aplusclick.orgImage

The Best Math Word Problems

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What are real-life math problems?

What are the funniest word problems?

What are the shortest word problems?

What are the most difficult word problems?

What are the best word problems?

Math and logic word problems. Here my preferred word problems go:

Practical:

How many tennis balls can fit in a school bus?

A goldfish need 1000 cubic inches of water to live in. 
An aquarium is 20 inches in diameter. 

How many fish can live in an aquarium?

Funny:

1 costs $10; 20 costs $20. How much does 100 cost?

99% of nuts and 99% of a nut cost as much as all nuts. How many nuts are there?

At least two Londoners have the same number of hair. Correct?

80% of IT projects fail, and 20% of managers are female. How many male managers succeed?

Short:

Does clock hands overlap 22 times in 24h?

How many zeros are at the end of 99!?

Make 33 by using three 3s and any signs.

Difficult:

Six Millennium Prize Problems set by the Clay Mathematics Institute have yet to be solved.

http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics

The Best:

Short + Funny + Practical + Difficult = Best

My preferred math and logic word problems are at www.aplusclick.org

The latest collection of the best free A+Click Puzzles are at Apple App Store

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Job Interview Logic Puzzles

Job Interview Logic Puzzles

JobInterviewLogicPuzzles

Job seekers encounter challenging logic and math puzzles in interviews at high-tech companies. Innovative companies such as Google, LinkedIn, Yahoo, and Microsoft use these types of questions to identify the most intelligent candidates. Microsoft is considered as a pioneer in the interview logic questions. The trend was initially based on Bill Gates’ obsession with puzzles, Fermi problems, and brainteasers. Fermi was known for his ability to make good approximate calculations with little or no actual data.

Winning matters

Puzzles test intelligence. You either get the answer, or you don’t… Logic puzzles divide the world into winners and losers. You get the job you deserve. Recruiters try to identify 3 groups of people 1) who are smart and get things done; 2) who are smart but don’t get things done; and 3) who get things done but are not smart.  It’s better to be on the smart side of the crowd.

How to become smart?

It’s simple. Train yourself like sportsmen build superior strength. Solve logic puzzles every day and never stop. Search for logic puzzles. This is a starter:  “Job Interview Logic Puzzles”  for iPad eBook or the “Job Interview Logic Puzzles” on Amazon. The book includes logic riddles, brainteasers, and spatial thinking questions, training people to confront unexpected questions, to think outside the box, and to elaborate upon non-standard solutions.

Is probability useful in real life?

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The question is simple. The best way to answer to the question is to give examples. Here they are:

How many cowboys are expected being alive after a gun fired in a saloon?

How many people in a block building have the same birthday as yours?

How much time do I expect to spend guessing a 5 digit password?

Does a prince have a chance to be chosen by a princess?

How much money does a casino earn everyday?

What is chance that a rocket launch will be successful?

Does a nuclear reactor explode if 4 of 100 its nuts fail?

We don’t use probability on daily basis. Sometimes, simple probabilistic calculations help us to make wise decision and avoid risk. My answer to the title’s question is YES. And yours?

A+Click SMS Part 3

A+ Click

SMS stands for Short Math Situation. The SMS questions are limited to 64 characters.

61. I cut & folded a shape of 1m square. What’s the largest volume? Answer

62. Make 33 by using three 3s and any math operators. Answer

63. How would you measure 4 liters with 3 and 5 liter buckets? Answer

64. Find 2 fractions made of 10 different digits. They add up to 1. Answer

65. Find the largest 2-digit perfect number. Answer

66. Find the maximum number of points of intersection of N circles. Answer

67. How do you cut a round cheese into 8 equal pieces with 3 cuts? Answer

68. Find the smallest 10-digit integer with only 2 digits the same. Answer

69. How many digits did I write to number 100 pages? Answer

70. How many squares can I form with 8 matchsticks? No overlap. Answer

71. What is the sum of the first 99 consecutive integer numbers? Answer

72. How many crosspieces do I needed to separately enclose 4 lambs? Answer

73. A Z D W G Find the next letter in the sequence. Answer

74. How many 4-digit passwords are possible if I use only 2 digits? Answer

75. How many 2-digit integers have the sum of the digits equals 10? Answer

76. The number A4321 is divisible by 9. Find the digit A. Answer

77. How thick is a plait of 200 hairs which diameter is 0.02 mm? Answer

78. What is the creases’ net on a paper folded in half 4 times? Answer

79. Find the smallest sum of 2 integers. Their product is 1000. Answer

80. What is the probability that two random dominos match? Answer

81. How many squares can be formed using seven matchsticks? Answer

82. Cut a rectangular piece of cheese with a hole in 2 equal parts. Answer

83. I met two kittens. What is the probability that they are boys? Answer

84. What number of spots appears more frequently on dominoes? Answer

85. Find 4 different integers if their product is 792? Answer

86. How many one-dollar bills completely cover a square mile? Answer

87. How many separate regions do three overlapping triangles form? Answer

88. How many letters are in the correct answer to this question? Answer

89. If 3 kids eat 3 kiwis in 33 seconds, how long do 9 kids eat 19? Answer

90. What sum of 2 digits is best to bet on? Answer

A+Click SMS Part 1 (questions 1 – 30)

A+Click SMS Part 2 (questions 31 – 60)

A+Click SMS Part 4 (questions 91 – 112)

A+Click SMS Part 2

A+ Click

SMS stands for Short Math Situation. The SMS questions are limited to 64 characters.

31. How many diagonals does a regular octagon have? Answer

32. How many times heavier than a rabbit is an elephant? Answer

33. If you live 100 years, how many times will your heart beat? Answer

34. How many handshakes take place at a 100 men meeting? Answer

35. How many 4-digit pass codes are there? All digits are different. Answer

36. What part of the American flag is red? Answer

37. 99% of N nuts and 99% of a nut cost as much as all nuts. Find N. Answer

38. Find the smallest number divisible by all numbers from 1 to 20. Answer

39. Work out the sum of all the integers below 100. Answer

40. I buy 5 eggs for $1 and sells 1egg for $5. What’s my profit? Answer

41. How to split $4, $5, and $6 in a ratio of 1:2:3? Answer

42. What is the probability that two kittens are boys? Answer

43. What is the probability that one of 3 idiots survives in a duel? Answer

44. At least 2 Londoners have the same number of hairs. Is it true? Answer

45. Is it possible to plant 10 trees in 5 rows of 4 trees? Answer

46. How many triangles can I make with six line segments on a plane? Answer

47. Divide $1234 into the ratio 1:2:3:4. Answer

48. How much costs an item after three successive discounts of 20%? Answer

49. One of 240 coins is odd. How do you use a scale to find it? Answer

50. Tom’s income and spending are 7/8 that of Tim. Who saves more? Answer

51. How many 11-digit numbers can you make using 0, 1? Answer

52. Find the smallest integer that is 4 times the sum of its digits. Answer

53. How many 0s are at the end of the product of 2-digit integers? Answer

54. Guesstimate the number of your ancestors in 200 years. Answer

55. How many tennis balls can fit in a school bus? Answer

56. O T T F F S S What is the next letter in this series? Answer

57. Find the angle between two diagonals of a cube. Answer

58. For which capital letter would you use more paint? Answer

59. How many $1 bills are numbered from AB01234567 to AB11111111? Answer

60. What occurs once in a minute, twice in a week, once in a year? Answer

A+Click SMS Part 1 (questions 1 – 30)

A+Click SMS Part 3 (questions 61 – 90)