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FC: Brainteasers | Original and Famous | By: Austin Passmore | + | Math Laws & Tricks

1: Table of Contents | Brainteasers.................................................................3 Original Brainteasers............................................................4 Solutions........................................................................12 Famous Favorites..................................................................17 Solutions.......................................................................25 Math Laws & Tricks.......................................................31 Original..................................................................................32 Famous Favorites..................................................................33 | 1

2: 2

3: Brainteasers | 3

4: 4 | Original Brainteasers | These brainteasers were created by me. They were inspired by brainteasers I have heard of since I was in kindergarten, Sam Loyd, and Raymond Smullyan. These brainteasers are dedicated to Mrs. Parker, Mrs. Wulz, Mrs. Turk, Mrs. Idol, Mrs. Brooksher, and Mr. Skogman. These teachers were the ones who got me hooked on brainteasers and math.

5: 5 | The Milk Convention Problem | Part One: | At the 2012 World Milk Convention in Atlanta, Georgia, a milking contest was held. The winner would be the owner whose animal would produce the most milk in 30 minutes. The contestants consisted of 19 goats, 20 yaks, and 1 squirrel. All of them recently had kids. After 30 minutes of milking, the winner was the squirrel, and its owner won $1,000. How could the squirrel have beaten all of the other contestants? | Part Two: | The next year, the 2013 World Milk Convention was in Miami, Florida. This year in the milking contest, 9 goats, 15 yaks, 15 cows, and the squirrel that won last year competed. All had recently had kids. After 30 minutes of milking, the winner was one of the cows, and its owner won $1,000. How could one of the cows have beaten all of the other contestants?

6: 6 | The Cubed Numbers | What positive rational whole number when cubed is less than when the number is multiplied by 3? | What number when cubed is neither greater or less than when the number is multiplied by 3?

7: 7 | The 4-Operation Number Pattern | 1, 2, -1, -1 1/2, -4, -7 2/3, ?, -12 13/138 | Find the 7th term if: n = 1; n = 2. | 1 | 2 | This is a number pattern using the four operations of math: addition, subtraction, multiplication, and division.

8: Big Ben's Face | A man named Doug had a dream to go to London to see Big Ben. When he earned enough money after 10 years, he went. He got there and started taking pictures when an English gentleman approached him and asked him a question. If Doug answered correctly, then he would award Doug with 700 pounds. His question was, "If Big Ben says it's 11:20 AM, how would you divide Big Ben's face into 4 congruent pieces where a part of one of his hands is in each fourth?" After a few minutes, Doug walked away with 700 pounds. What was his answer? | 8

9: The Magic Diamond | Using five consecutive numbers, put a number in each circle. The digits of a triangle made of three digits must be multiplied together so that the product is the same for every triangle made of three. Also, the digits of every triangle made of four must be multiplied together so that the product of each triangle made of four is the same and is twice as much as the product of the digits that make a triangle of three. | 9

10: The Way to Belgathor | You walk down a road and come to a fork in the road. One sign points to the left and the other sign points to the right. Of the two signs, one is truthful and the other is false, but you don't know which is which. Between the two signs, there are three signs. Of the three signs, exactly two are lying. | If you are trying to get to Belgathor, which way would you go using the signs and why? | 10

11: Belgathor is not this way. | Belgathor is not this way. | 1 | 2 | 3 | 4 | 5 | Sign 1 is lying. | Sign 1 is telling the truth. | If Sign 3 lies, then Sign 4 lies. | 11

12: Solutions | The Milk Convention | Part One: | The squirrel won because it was the only female. Even though every contestant recently had kids, it didn't mean that all of the contestants actually gave birth to their kids. | Part Two: | A cow won because it produced the most milk in 30 minutes. The squirrel wouldn't be the only female because a cow has to be a female. | 12

13: The Cubed Numbers | The positive rational whole number when cubed is less than when the number is multiplied by 3 is 1. | The number when cubed is neither greater or less than when the number is multiplied by 3 is 0. | The 4-Operation Number Pattern | The 7th term is equal to | -10 7/12. | 13

14: Big Ben's Face | 14

15: The Magic Diamond | 0 | 1 | 2 | -1 | -2 | This brainteaser has multiple answers, but the one thing that must stay constant between every answer is that 0 must be in the center of the "Magic Diamond". | 15

16: The Way to Belgathor | To start, we must determine which of the three signs are lying. To begin that, we must determine whether Sign 5 is lying. Because Sign 3 and Sign 4 contradict each other, one of them must be false which also means that Sign 5 is the other false sign. Also because Sign 3 and Sign 4 contradict themselves, the "If" statement and the "then" statement are opposites, meaning that one of the statement is lying and the other is truthful. The only way that Sign 5 can be lying is if the "If" statement is truthful and the "then" statement if false. Knowing this, we also know that Sign 3 is lying and Sign 4 must be telling the truth. This allows us to determine that Sign 1 is truthful and that "The Way to Belgathor" is by taking the path to the right. | 16

17: Famous Favorite Brainteasers | These are some of my favorite brainteasers that I have enjoyed attempting to solve. Some of these have been either shown to me by one of the teachers I dedicated my brainteasers to or by personal research. I hope readers will enjoy them as much as I have. | 17

18: The Famous Elevator Puzzle | A man who lives on the tenth floor of an apartment building takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment. Can you explain why? | 18

19: The Light Bulb Puzzle | On a wall there are 3 standard on/off switches. One (and only one) controls a light bulb inside a light-tight, well-insulated closet. The other two switches do nothing. You can only open the closet door once, and cannot touch/change any switches after the door is open (or re-closed, for that matter). Damaging or disassembling the door, walls, or switches is against the rules. Within these constraints, can you determine with certainty which switch controls the light bulb? | 19

20: Cutting the Cake Brainteaser | You must cut a birthday cake into exactly eight pieces. However, you are only allowed to make three straight cuts, and you cannot move pieces of the cake as you cut. How can you do it? | 20

21: The Canals of Mars | By: Sam Loyd | Here is a map of the newly discovered cities and waterways on our nearest neighbor planet, Mars. Starts at the city marked T, at the south pole, and see if you can spell a complete English sentence by making a tour of all the cities, visiting each city only once, and returning to the starting point. When the puzzle originally appeared in a magazine, more than fifty thousand readers reported, "There is no possible way." Yet it is a very simple puzzle. | 21

22: One man left to his four sons a square field with four ancient oak trees served as landmarks. This tract of land is shown in the figures above. The sons were instructed to divide the field into four pieces of the same size and shape, and so that each piece of land contains one of the oak trees. The sons were unable to divide the land properly, and finally squandered the estate. It's a very old story known as the "battle of the four oaks". But the task still remains: how can it be done? Try to find the right solution for this classic puzzle. | The Battle of the Four Oaks | By: Sam Loyd | 22

23: The Quarrelsome Neighbors | It is told that three neighbors who share a small park, as shown in the sketch, had a falling out. The owner of the large house, complaining that his neighbor's chicken annoyed him, built an enclosed pathway from his door to the gate at the bottom of the picture. Then the man on the right built a path to the gate on the left, and the man on the left built a path to the gate on the right. None of the paths crossed. Can you draw the three paths correctly? | By: Sam Loyd | 23

24: The Young Carpenter's Puzzle | The picture tells its own story and does not require a Sherlock Holmes to tell us that the lads have found an old tool chest in the garret; that their mother is attending an afternoon meeting, and that it must be Thursday, when Bridget has her day out. There are other interesting features which suggest themselves, such as how Towser is to get out of the little door after the kids have nailed up the side of the dog house. That, however, is a problem for Towser to settle in his own way, so we will waste no time in getting to the real point of the puzzle. What is the best way of cutting the square top of the kitchen table into the fewest number of pieces which will fit together so as to close up the open end of the dog house? | By: Sam Loyd | 24

25: Famous Favorites Solutions | The Famous Elevator Puzzle | The man is a of short stature. He cannot reach the upper elevator buttons, but can push is with his umbrella on a rainy day. | 25

26: The Light Bulb Puzzle | Turn on switch "A" for 5 minutes. Turn it off and turn on switch "B". Open the door and touch the light bulb. 1. If the light bulb is on, it is "B". 2. If the light bulb is off and hot, it is "A". 3. If the light bulb is off and cold, it is "C". | 26

27: Cutting the Cake Brainteaser | The Canals of Mars | The fifty thousand readers who reported "There is no possible way" had all solved the puzzle, for that is the sentence that makes a round trip tour of the planet! | 27

28: The Battle of the Four Oaks | This brainteaser inspired me to make "Big Ben's Face". | 28

29: The Quarrelsome Neighbors | 29

30: The Young Carpenter's Problem | 30

31: Math Laws & Tricks | 31

32: Original | I came up with this number trick one day when i was playing around with a calculator trying to come up with a brainteaser. I call it Passmore's Rule. This rule works with 2 to 5-digit numbers. If a 3-digit's digits are intervals of 3, ex: 147 or 369, then if you take that number, add 1 to every digit, and reverse the order, it will add together to the 1st number and create a sum that has digits that will all be the same or it will create a palindrome. This will work with a 2-digit number if the digits are intervals of 4, a 4-digit number if the digits are intervals of 2, and a 5-digit number if the digits are intervals of 1. Ex: 147 + 852 = 999 12,345 + 65,432 = 77,777 357 + 864 = 1,221 This rule will not work if the digits exceed pass 9. Ex: 579 + 1,086 = 1665 | 32

33: Famous Favorites | Determine Your Birthday | Add 18 to your birth month Multiply by 25 Subtract 333 Multiply by 8 Subtract 554 Divide by 2 Add your birth date Multiply by 5 Add 692 Multiply by 20 Add only the last two digits of your birth year Subtract 32940 to get your birthday! The answer’s format is: month/day/year. For example, an answer of 123199 means that you were born on December 31, 1999. If the answer is not right, you followed the directions incorrectly or lied about your birthday. | Ex: My birthday (Jan. 24, 1997) 1 + 18 = 19 19 x 25=475 475 - 333 = 142 142 x 8 = 1136 1136 - 554 = 582 582 / 2 = 291 291 + 24 = 315 315 x 5 = 1575 1575 + 692 = 2267 2267 x 20 = 45340 45340 + 97 = 45437 45437 - 32940 = 12497 | 33

34: Grey Elephants in Denmark | Pick a number between 1 & 10. Multiply by 9. If the result is a two digit number, add the two digits together. Subtract 5 from the resulting number. Beginning with the letter A as 1, count over in the Alphabet that many letters ( I usually will count a few out loud " A is 1, B is 2, C is 3.") Now think of a Country that begins with your letter (Only big Baseball fans, or Cigar smokers will get the Dominican Republic, the rest will get Denmark) Take the second letter in your county and think of a Circus Animal that begins with that letter. Wait a couple of seconds and Declare "There are no Elephants in Denmark!" Explanation: The result of step 3 (adding together the digits of a multiple of nine) will always yield "9", so subtracting 5 yields 4, which in turn forces the letter "D". | 34

35: Interesting Sequentials | Sequential Inputs of numbers with 8 1 x 8 + 1 = 9 12 x 8 + 2 = 98 123 x 8 + 3 = 987 1234 x 8 + 4 = 9876 12345 x 8 + 5 = 98765 123456 x 8 + 6 = 987654 1234567 x 8 + 7 = 9876543 12345678 x 8 + 8 = 98765432 123456789 x 8 + 9 = 987654321 | Sequential 1's with 9 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 123456 x 9 + 7 = 1111111 1234567 x 9 + 8 = 11111111 12345678 x 9 + 9 = 111111111 123456789 x 9 + 10 = 1111111111 | Sequential 8's with 9 9 x 9 + 7 = 88 98 x 9 + 6 = 888 987 x 9 + 5 = 8888 9876 x 9 + 4 = 88888 98765 x 9 + 3 = 888888 987654 x 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888 | Numeric Palindrome with 1's 1 x 1 = 1 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 111111 x 111111 = 12345654321 1111111 x 1111111 = 1234567654321 11111111 x 11111111 = 123456787654321 111111111 x 111111111 = 12345678987654321 | 35

36: Zero to the Zero Power | It is commonly taught that any number to the zero power is 1, and zero to any power is 0. But if that is the case, what is zero to the zero power? Well, it is undefined (since x as a function of 2 variables is not continuous at the origin). But if it could be defined, what "should" it be; 0 or 1? | y | 36

37: Kaprekar's Constant | Take any four digit number (whose digits are not all identical), and do the following: Rearrange the string of digits to form the largest and smallest 4-digit numbers possible. Take these two numbers and subtract the smaller number from the larger. Use the number you obtain and repeat the above process. What happens if you repeat the above process over and over? Let's see... Suppose we choose the number 3141. 4311-1134=3177. 7731-1377=6354. 6543-3456=3087. 8730-0378=8352. 8532-2358=6174. 7641-1467=6174... The process eventually hits 6174 and then stays there! But the more amazing thing is this: every four digit number whose digits are not all the same will eventually hit 6174, in at most 7 steps, and then stay there! | 37

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