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Math can be cool, complex, and even magical! If you’ve ever wanted to impress your friends with an awesome math trick, show your students the fantastical possibilities of math, or simply improve your own mathematical skills, you’ve come to the right place! We’ve put together a comprehensive list of the best mental math tricks and magical math illusions for any time and any place.
What’s the most mind-blowing math trick?
There are tons of great math tricks out there, but one of the best is the 1089 trick, where you’ll always get the result 1089 by following this set of steps:
- Pick any 3-digit number where the first and last digits are at least 2 apart (e.g., 235).
- Reverse the number (e.g., 532).
- Subtract the first number from the second one (e.g., 532 – 235 = 297).
- Reverse the result (e.g., 792).
- Add the subtracted difference and its reversal together (e.g., 297 + 792 =1089).
Steps
- This trick is specifically for a special group of people born in 1998…and it’s sure to wow them! If you were born in 1998, start by picking any number between 1 and 7. Multiply this number by 2, add 5, and multiply the new result by 50. If you’ve already had your birthday this year, add 1748. If you haven’t, add 1747. Next, subtract 1998 to get a 3-digit number. The first digit of this number will be your original number, and the last two digits will be your age.
- Thiscool math trick is actually used to validate credit card numbers and catch typos, but you can test it out on your own credit card! Start with a 15- or 16-digit credit card number. Then, starting from the second-to-last digit, move from right to left and double every other digit. Then, add all of the new doubled digits to the digits that werenot doubled. If the total sum ends in 0, the card number is correct and valid![1]XResearch source
- If, in the first step, your doubling results in any number being greater than 9, add the two digits together to create a single digit example.
- Example:
- Let’s say the credit card number is 79927389713.
- Double every second digit from the right → 6, 1, 5, 8, 6, 7, 4, 9, 9, 7.
- Add up all the numbers → 7 + 9 + 9 + 4 + 7 + 6 + 9 + 7 + 7 + 2 + 3 = 70.
- 70 ends with a 0, so this is a valid number!
- It’s actuallysuper helpful to count on your fingers…at least when it comes to multiplying! To multiply numbers by 9 with this TikTok-viral trick, just place both hands in front of you with your thumbs and fingers extended, says math expert David Jia. If you want to multiply 9 by any one-digit number, continues Jia, count your fingers from the left and fold down the finger that corresponds to the one-digit number. Then, count the fingers on either side of the folded one to get each digit of your answer.[2]XExpert Source
David Jia
Math ExpertExpert Interview- Example:
- Let’s multiply 9 by 5.
- Fold down your fifth finger from the left (i.e., the thumb of your left hand).
- Count the number of fingers on the left side of the “fold” (4).
- Count the number of fingers on the right side of the “fold” (5).
- Your resulting answer is45.
- Example:
- Tell a group of friends or students that you’re going to try toread their minds—then, write “grey elephants from Denmark” on a piece of paper, don’t show it to anyone, and place it face down on a table. Then, talk your group through the following prompts, and reveal the sentence on your paper at the end of the activity:[3]XResearch source
- Think of a number from 2 to 10.
- Multiply your number by 9.
- Add the two digits of your result together.
- Subtract 5 from your answer.
- If your answer is 1, it equals A. If it’s 2, it equals B. If it’s 3, it equals C. If it’s 4, it equals D.
- Think of a country in Europe that begins with your letter.
- Think of an animal that’s not a bird or a fish that begins with the second letter of your country.
- Think of the color of your animal.
- In this math trick, every final result will contain the digits 1, 2, 4, 5, 7, and 8. Start with a number between 1 and 6. Then, multiply that number by 9, multiply your result by 111, multiply again by 1001, and divide that answer by 7.
- Example:
- Let’s say your starting number is 3.
- Multiply by 9 → 27.
- Multiply by 111 → 2,997.
- Multiply by 1001 → 2,999,997.
- Divide by 7 →428,571.
- Example:
- Ask someone to secretly write down their Social Security Number (or any 9-digit number), then have them scramble up all the digits and write it down again. If there are any zeroes in their number, have them change them to any other number between 1 and 9. Then, have them copy their nine numbers, in order, next to their original (unscrambled) nine numbers. Now, they’ll have an 18-digit number where the first half is the same as the second half.
- Now, have them change thesecond digit of their number to a 7, and change theeleventh digit to a 7.
- Now, challenge them to a race to see who can figure out the answer to that number divided by 7.
- If they start trying to divide by hand, you can beat them to it! The answer is alwayszero, because 7 will always divide exactly into this new number (with nothing left over).
- You’ll need a regular, well-shuffled deck of cards for this trick. After shuffling your cards thoroughly, deal 36 cards into a pile, then ask a friend to pick one of the cards, memorize it, and put it back in the pile (without showing it to you). Then, shuffle the 36 cards and lay them out in 6 rows of 6 cards each. Deal each row from left to right. Next, ask your friend to look at the cards and tell them whichrow their card is in.
- Then, carefully pick up the cards in the same order you placed them down in.
- Lay the cardsagain in 6 rows of 6 cards each, but place them down one column at a time (rather than one row at a time). Place the first six cards in a column from top to bottom, then repeat this process to create six columns from left to right.
- Again, have your friend look at the cards and tell which row their card is in.
- Use your friend’s information to ~divine~ their card.For example, if their card was in row 2 and then in row 5, their card isnow in the second column of the fifth row.
- If you want to memorize the first seven digits of pi, use the phrase “How I wish I could calculate pi.” Each word in this sentence has the same number of letters as its corresponding digit in pi. The first seven digits of pi are 3.141592. “How” has 3 letters, “I” has 1, “wish” has 4, and so on.[4]XResearch source
- Did you know that if you multiply 6 byany even number, the answer will always end with the same digit as the even number? This little trick makes it super easy to calculate your sixes![5]XResearch source
- Example:
- 6 x4 = 24
- 6 x 10 = 60
- 6 x 16 = 96
- Example:
- An easy way to remember the multiples of 9 is to use the “minus 1” rule. Let’s say that “N” represents any given number between 1 and 9. If you’re multiplying 9 times N, the tens digit of the result isalways N – 1, and both digits will always add up to 9. For example, 9 times 3 is 27. The number 2 is in the tens digit, which is also equal to N – 1 (i.e., 3 – 1). And, 2 + 7 equals 9!Here are the rest of the key multiples of 9:
- 9 X 1 = 09
- 9 X 2 = 18
- 9 X 3 = 27
- 9 X 4 = 36
- 9 X 5 = 45
- 9 X 6 = 54
- 9 X 7 = 63
- 9 X 8 = 72
- 9 X 9 = 81
- Have someone choose any three-digit number where each digit is the same (e.g., 111, 555, 888, etc.). Add up all of the digits within that number to get a sum. Then, divide the original three-digit number by that sum. The answer will ALWAYS be 37—why? The sum of the digits will always be three times the digit itself, and each three-digit number is a multiple of that digit and 111. So, in the last step, you’re canceling out the digit, and you’re left with 111 divided by 3, which is 37![6]XResearch source
- Example:
- Let’s say your number is 333.
- Add up all the digits → 3 + 3 + 3 = 9.
- Divide the number by the sum → 333 / 9 =37.
- Example:
- Take any three-digit number and write it twice to create a six-digit number (e.g., 435435, 938938, etc.). Divide that number by 7, then divide the result by 11, then dividethat result by 13. Your final answer will be your original three-digit number, because you’re basically dividing by 1,001, which will always give you the three-digit version of the number.
- Example:
- Let’s say your number is 284284.
- Divide by 7 → 40,612.
- Divide by 11 → 3,692.
- Divide by 13 →284.
- Example:
- Let’s say you have a (very) large number of pizza slices and want to know whether or not you can evenly split them amongst your group. You can use some simple division shortcuts (listed below) to do the math in your head!For example, if you have 210 pieces of pizza, you can use the tricks below to figure out that the pizza could be easily divided amongst 2, 3, 5, 6, or 10 people.Here are the shortcuts:[7]XResearch source
- Your pizza is divisible by2 if the last digit is a multiple of 2.
- Your pizza is divisible by3 if the sum of the digits is divisible by 3.
- Your pizza is divisible by4 if the last two digits are divisible by 4.
- Your pizza is divisible by5 if the last digit is 0 or 5.
- Your pizza is divisible by6 if it passes the rules forboth 2 and 3.
- Your pizza is divisible by9 if the sum of the digits is divisible by 9.
- Your pizza is divisible by10 if the number ends in a 0.
- Your pizza is divisible by12 if it passes the rules forboth 3 and 4.
- The viral 1089 trick always gives you a result of 1089, confirms professional magician Magic Suzy, if you follow a specific routine of switching numbers and using addition and subtraction.[8]XExpert Source
Magic Suzy
Professional MagicianExpert Interview To do the trick, pick any 3-digit number where the first and last digits differ by at least 2. Reverse the order of the digits, then subtract the first number from the new (reversed) one. Reverse the result of the subtraction, then add the original subtraction to its reversed version. You should get 1089 as your answer!- Example:
- Let’s start with the number 235.
- Reverse it → 532.
- Subtract the two numbers → 532 – 235 = 297.
- Reverse the result → 792.
- Add the subtraction & reversal together → 297 + 792 =1089.
- Example:
- If you want to easily multiply two-digit numbers by 11 withmental math, this is the trick to do it! Start by separating the two-digit number in your mind. Then, add the two digits together and place the resulting sum between the two digits. If your sum was greater than 9, put the second digit in the in-between space and carry the first digit. This should give the correct multiplication product![9]XResearch source
- Example:
- Let’s calculate 43 x 11.
- Separate the two-digit number → 4, 3.
- Add the digits together → 4 + 3 = 7.
- Place the sum between the two digits →473.
- Example:
- This amazing trickalways results in an answer of 18. Ask someone to secretly come up with three different numbers, all of which need to be between 1 and 9. Then, have them write the three numbers down next to each other from largest to smallest to form a single 3-digit number (make sure they don’t show you the number or the paper!). Next, have them reverse the digits, so that the smallest is first and the largest is last. Ask them to write this new number underneath the first one.
- Then, have them subtract the lower 3-digit number from the upper one, keeping the result a secret.
- Ask them to then add up the three digits of their result, then tell them that their sum is 18! Because it always will be!
- Example:
- Let’s start with 1, 4, and 6.
- Write the three numbers from largest to smallest → 641.
- Write them from smallest to largest → 146.
- Subtract the second number from the first one → 641 – 146 = 495.
- Add up the three digits of the difference → 4 + 9 + 5 =18.
- First, think of any number (or ask someone else to think of a number—but tell them to prepare for their mind to be blown!). Then, multiply it by 3, then add 6, then divide the resulting number by 3. Finally, subtract the original number from your current result. The answer will be 2…because the answer isalways 2! This trick works because, in the last step, you’re cancelling out the number you originally came up with. You’re also canceling out a step when you multiplyand divide by 3 in separate steps. So, you’re basically just dividing 6 by 3, which will always give you 2![10]XResearch source
- Example:
- Let’s say your number is 10.
- Multiply the number by 3 → 30.
- Add 6 → 36.
- Divide by 3 → 12.
- Subtract the original number → 12 – 10 =2.
- Example:
- Ready to impress everyone you know with some psychic skills? The next time you’re with a group of people, assign each person a number from 1 to whatever the total number of people in the group is. Then, get a piece of string, and tell the group to tie the string onto someone’s finger while you’re out of the room or not looking. Then, tell them that you can divine who has the string, which hand it’s on, and which finger it’s on. To achieve this goal, ask one person in the group to answer the following questions for you:
- Multiply the number of the person with the string by 2.
- Add 3 to that result.
- Multiply by 5.
- If the string is on the right hand, add 8. If it’s on the left, add 9.
- Multiply by 10.
- Add the number of the finger (thumb = 1, index = 2, middle = 3, etc.).
- Add 2.
- Have them tell you the answer, then mentally subtract 222. The difference will give you your answer:
- The rightmost digit corresponds to the finger that the string is on.
- The middle digit will be 2 if it’s on the left hand, and 1 if it’s on the right hand.
- The leftmost digit tells you the number of the player who has the string.
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References
- ↑https://www.scientificamerican.com/article/what-is-the-luhn-algorithm-the-math-behind-secure-credit-card-numbers/
- ↑David Jia. Math Expert. Expert Interview
- ↑https://www.cambridge.org/elt/blog/2019/08/09/grey-elephants-denmark/
- ↑https://markseducation.com/wish-calculate-pie/
- ↑https://www.cuemath.com/learn/math-tricks/
- ↑https://www.cuemath.com/learn/math-tricks/
- ↑https://nrich.maths.org/problems/it-magic-or-it-maths
- ↑Magic Suzy. Professional Magician. Expert Interview
- ↑https://nrich.maths.org/problems/it-magic-or-it-maths
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