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?

 

 

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Brain Teaser Interview Questions and Answers

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Brain Teaser Interview Questions and Answers

answers brain teaser interview questions that are commonly asked at job interviews for technical and quantitative roles. These questions focus on problem solving, spatial reasoning, and understanding.

By reading this document, you’ll be better prepared to answer unexpected questions, think outside the box, and elaborate on non-standard solutions. And most importantly, you’ll be calm and relaxed at the interview.

Answers to  brain teaser interview questions including:

    • How do you find your car along a very long street when you don’t remember where you parked it?
    • We want to merge 4 companies into one large company. How many ways are there to merge them?
    • I have a rectangular piece of cheese with a round hole. How do I cut the piece with one straight lien into two parts of equal weight?
    • There are a number of stones, all of different weights. The 10 lightest stones weigh 40% of the total weight. The 5 heaviest stones weigh 25% of the total weight. How many stones are there?
    • What is the avg. of the smaller of three random numbers of 0 to 1?
    • “1” costs $10. “20” costs $20. How much does “100” cost?
    • It takes 6 people 48 hours to paint a house. How long would it take to paint the house if 3 people were added to the middle of the project?
    • 3 apples were weighed in pairs and the weights were 200, 204, 208 grams. What is the weight of the lightest apple?
    • You are shrunk so that your height is equal to the diameter of a dime (a ten-cent coin) and your mass is proportional reduced so as to maintain your original density. Who is heavier, you or the dime?
    • I roll two dice. What is the probability that the 2nd number is greater than the 1st?

Funny Questions and Unexpected Answers at Tech Job Interview

Brain Teaser Interview Questions And Answers on Amazon

Brain Teaser Interview Questions And Answers on iTunes

Mr Barton’s Web Whizz Video on A+ Click Math

“I love NRICH, & whilst it remains my number one stop for rich maths puzzles & problems, this website might just be number two. There are literally 100s of puzzle & problems for students to solve. They are beautifully laid out on the page, making them absolutely ideal to project on the board to use as starter activities or extension work. I also suggest using them in the computer room as the website keeps a handy record of students’ progress through a series of puzzles. With the development of students creative thinking & problem solving growing in importance, this website is a must!” – Craig Barton

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.

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)