Pancake Math

panecake2“Archaeological evidence suggests that pancakes are probably the earliest and most widespread cereal food eaten in prehistoric societies.” – Wikipedia

 

What is the maximum number of sections into which a pancake may be divided into by four straight cuts through it?

Here more difficult questions go:

1) Is it possible to divided it so that all sections have equal area?

2) How many pancakes are needed to reach your height if they are squeezed by the weight of the upper pancakes?

3) If I spent 30 grams of batter for a pancake (French-style crêpe) of 30 cm in diameter how much batter do I need for the square pancake of the same thickness and the side length of 30 cm?  

 

These and many other practical “pancake” questions are presented in the Applied Math section of A+Click series, which already includes more than 4500 questions.

 

SAT Math

Aplusclick has just published a new free collection of 150+ SAT Math questions at www.aplusclick.com/sat.htm.

AplusclickSATMath

Math Magic: To Predict Unknown

Image

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?

 

 

No Math. No Problem!

John said:

No Math . . .  No Problem!

Real Word vs Math Word ???

SAT is a measure how much rich the guy’s parents are.

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

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)

A+Click SMS

A+ Click

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