A+Click SMS Part 3

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)

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A+Click SMS Part 2

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)

Does the car owner need math?

Many car owners make decisions without any calculation. They use gut feelings and don’t spend time on math. However, small calculative efforts of 2-3 minutes can help to inform wise decisions and give the owner the confidence that they are making the best choice.

Here are real-life examples:

We calculate how many miles we can drive with a half tank.

We calculate the value of a car after owning it for several years.

We compare cars when we want to choose one that is fuel-efficient.

We calculate the potential costs when we decide to rent or buy a car.

We calculate the profit and losses when buying or selling cars.

Estimate how many miles can you drive if you change the tires (front <-> back) at the best moment. Rear tires of your car wear out after 60,000 miles, while the front tires wear out twice faster.

We accept or refuse bids when selling cars.

In the last case, you don’t need to know the complex optimal choice theory and its formulae. It’s enough just to keep in mind several simple rules that help you to make wise decisions. People who spend a few minutes on simple calculations always enjoy their choice.

Calculate or guess? The answer is YES.

When required to make a decision, I have the option to produce simple calculations, guess, or even refuse to decide. What is better?

The answer depends on many circumstances, including:

• Complexity of the challenge.
• Usefulness of the conclusion.
• Individual ability / habits to analyze challenges.
• Time available.

I meet difficult challenges very often. What technique should I use? Should I work it out or should I guess?

Calculations are beneficial in terms of time and money in the following examples:

• Which company should I invest in?
• Which company pays their employees better?

I am ready to spend my time on simple analysis and calculation in such cases.

Weinstein and Adam [1] advise guesstimating certain categories of challenges. A guesstimate is an informal English contraction of guess and estimate and is used to describe an estimate made without complete information. Another term for this is an educated guess at something for which no better information will become available.

There are a group of challenges called “Fermi problems” (after the great nuclear physicist) that will be accurate to within an order of magnitude. A mistake of up to 10 times is acceptable. The examples are:

• How many people will potentially buy a new car next year in a city?
• How many gas stations between Boston and New York?
• How many people will come to buy my car if I advertize on the Internet?
• How many tennis balls can fit in a school bus?
• What score does John expect to receive on the exam?
• How long is Anna’s hair?
• How many times heavier than a rabbit is an elephant?
• How many customers visit a shop everyday?

I need to guesstimate in order to answer such questions.

The answer to the question in the title “Calculate or Guess?” is yes. I calculate when I have time and the ability, I guesstimate when a conclusion with order of magnitude is acceptable, and I trust my gut feeling in all other cases.

1. Lawrence Weinstein and John A. Adam, Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin. 2008 Princeton University Press. ISBN 9780691129495

A+Click SMS

SMS stands for Short Math Situation.

Don’t confuse with SMS (Short Message Service), which is used as an acronym for all types of short text messaging. The last one is the most widely used data application in the world with several billion active users.

If the length of the SMS text messages is limited to 140 characters, the Short Math Situation questions are limited to 64 characters. Everything should be made as short as possible, but no shorter.

A+Click SMS are:

1. Using 8 eights and addition only, please make 1000. Answer

2. How many inner right angles are possible in a hexagon? Answer

3. How many planes of symmetry does a cube have? Answer

4. How many planes of symmetry does an Egyptian pyramid have? Answer

5. What is the last digit of the number 7 power 77? Answer

6. How many zeros are there at the end of 99! ? Answer

7. How many squares can you make using twelve matches? Answer

8. Find the hundreds digit of the product: 4444444 x 9999999. Answer

9. Find the smallest sum of 2 integers if their product is 1000. Answer

10. What is the units digit of 1! + 2! + 3! + … + 2012! ? Answer

11. How many 1x2x3 boxes can be packed into a 5x6x7 box? Answer

12. How many times do a clock’s hands overlap in a day? Answer

13. How many zeros are there at the end of 100! ? Answer

14. What is the sum of the digits of all 2-digit numbers? Answer

15. Which product of 2 random dice numbers is best to bet on? Answer

16. Find the average of the smaller of 2 random numbers from 0 to 1. Answer

17. Find the average of the smaller of 3 random numbers from 0 to 1. Answer

18. Which 3-digit number has the greatest number of divisors? Answer

19. How many three-digit multiples of 7 end with digit 4? Answer

20. How many three-even-digit numbers are divisible by 9? Answer

21. What is the largest digit in the product of 11111111 x 11111111? Answer

22. Counting from 11 by 1, which number comes next? It is not 12. Answer

23. What is the largest product of integers that add up to 17? Answer

24. F = (x-a)(x-b)(x-c) . . . (x-x)(x-y)(x-z). Find F. Answer

25. 52 – 28 = 4 Which digit do I move to make the equation correct? Answer

26. Please make 121 by using three 5s any math operators. Answer

27. How many 3-digit numbers have 5 divisors including 1? Answer

28. Find the odd one out. DEMON FIRST FORTY GHOST Answer

29. Cut a rectangle with a round hole into two equal-area parts. Answer

30. How many digits are there in binary presentation of 999? Answer

A+Click SMS Part 2