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# Math Magic Tricks With Algebra

## Six Digits Become Three

Algebra Trick to save you time (Algebra Tricks)
• Take any three-digit number and write it twice to make a six-digit number. Examples include 371371 or 552552.
• Divide the number by 7.
• Divide it by 11.
• The order in which you do the division is unimportant!

The answer is the three-digit number.

Examples: 371371 gives you 371 or 552552 gives you 552.

• A related trick is to take any three-digit number.
• Multiply it by 7, 11, and 13.
• The result will be a six-digit number that repeats the three-digit number.

Example: 456 becomes 456456.

This is a quick way to multiply two-digit numbers by 11 in your head.

• Add the two digits together.
• Place the number from Step 2 between the two digits. If the number from Step 2 is greater than 9, put the one’s digit in the space and carry the ten’s digit.
• Examples: 72 x 11 = 792.

57 x 11 = 5 _ 7, but 5 + 7 = 12, so put 2 in the space and add the 1 to the 5 to get 627

## Super Simple Divisibility Rules

You’ve got 210 pieces of pizza and want to know whether or not you can split them evenly within your group. Rather than whip out the calculator, use these simple shortcuts to do the math in your head:

• Divisible by 2 if the last digit is a multiple of 2 .
• Divisible by 3 if the sum of the digits is divisible by 3 .
• Divisible by 4 if the last two digits are divisible by 4 .
• Divisible by 5 if the last digit is 0 or 5 .
• Divisible by 6 if it passes the rules for both 2 and 3 .
• Divisible by 9 if the sum of the digits is divisible by 9 .
• Divisible by 10 if the number ends in a 0 .
• Divisible by 12 if the rules for divisibility by 3 and 4 apply.

Example: The 210 slices of pizza may be evenly distributed into groups of 2, 3, 5, 6, 10.

## Check Out Some Mind Blowing Math Magic Tricks

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20 January 2021

Reading Time: 4 minutes

Math magic tricks can engage even the most distracted group of students and stimulate their senses to create a sense of wonder in their curious brains. Using such tricks sets up a strong foundation for students to strengthen their mathematical reasoning and go beyond just the routine textbook questions and answers.

Math is all about logic, rules, and reasoning, and to make the understanding of complex concepts easier, it is best to serve these concepts with a side of magic.

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## Diaconis Mind Reading Trick

I also heard from Mark Gorseky this description of a mathematical based card game

“Mark described a card trick of Diaconis where he takes a deck of cards, gives it to a person at the end of the room, lets this person âcutâ the deck and replace the two parts, then asks many other people do the same and then asks people to take one card each from the deck. Next Diaconis is trying to read the mind of the five people with the last cards by asking them to concentrate on the cards they have. To help him a little against noise coming from other minds he asks those with black cards to step forward. Then he guesses the cards each of the five people have.

I think there is a paper by Goresky and Klapper about a version of this magic and relations to shift registers.

## Multiplication At Your Fingertips

Did you know that you can effectively multiply any number of digits using your hands?

A simple way to do the “9” multiplication table is to place both hands in front of you with fingers and thumbs extended.

To multiply 9 by a number, fold down that number finger, counting from the left.

For example – to multiply 9 by 5, fold down the fifth finger from the left. Count fingers on either side of the “fold” to get the answer. In this case, the answer is 45.

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## Guess Their Age And Shoe Size

Ask your child to follow the given directions but not present any of the calculations to you –

Ask them to write down their age Multiply it by 1/5 of 100.Add on today’s date .Multiply by 20% of 25.Now add on your shoe size .Finally, subtract 5 times today’s date.

Ask them to reveal the final answer – The hundreds are the age and the remaining digits are the shoe size. If for instance, somebody shows you 1206, there are 12 hundred – the age, and the remaining digits 06 denote their shoe size.

## Multiply Large Numbers In Your Head

Another math magic tricks and methods to apply to easily multiply two double-digit numbers, is to use their distance from 100 to simplify the math:Subtract each number from 100.Add these values together.100 minus this number is the first part of the answer.Multiply the digits from Step 1 to get the second part of the answer.

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## I Know How Much Money You Got

Without giving you any information, ask the students to count the value of a random set of coins and write the amount on a piece of paper. Then ask them to follow the next steps-

Double the amount.Add the first odd prime number to the new total.Multiply the result by 1/4 of 20.Subtract the lowest common multiple of 2 and 3.

For the final answer – Take off the last digit and you will be able to guess how much the coins are worth!

## Other Types Of Math Tricks

Math Magic Trick

You can find math tricks in

 What do you get when you cut a Mobius strip in half?
• calendars
• a deck of cards
• handmade cards with specially created sets of numbers
• everyday objects: Introduce students to a realm of mathematics they might never have heard of — topology — as they ooh and ahh over paper clips leaping and linking together when a dollar bill is snapped, or over the wonders of a Mobius strip.

The resources at the end of this article encompass a variety of ideas presented in kid-friendly fashion.

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## How Did You Do That

For the most part, the resources cited in this article do not explain their tricks, because “Magicians never reveal their secrets!” You might choose for the tricks to stay in the realm of magic, to intrigue and delight your students. There can be value enough in students’ enthusiastic manipulation of numbers as they are being wowed. But there can be value, as well, in revealing a few magicians’ secrets.

Most math tricks can be understood with algebraic reasoning. Students as young as fourth grade can grasp how simpler tricks work if you guide them step by step through the reasoning and explain the algebraic notation. For example, the first trick can be explained like this:

 Think of a number between 1 and 100. Let’s represent this number as n. Multiply your number by 4. We can show this as 4n . Add 12.

## How To Do A Math Magic Trick

Everyone knows magic tricks are fun, but not enough people realize that math can be as well.XResearch source Whether you’re teaching students or just having fun with your friends, these tricks will give them a good surprise.

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## How To Do A Cool Mathematical Mind Reading Trick

wikiHow is a wiki, similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 20 people, some anonymous, worked to edit and improve it over time. This article has been viewed 392,883 times.

Mathematical mind reading tricks are a great way to combine your mastery of math with a bit of magical fun.

## Math Tricks That Will Blow Your Mind

• Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
• B.A., Physics and Mathematics, Hastings College

Are you ready to give your mathematics skills a boost? These simple math tricks can help you perform calculations more quickly and easily. They also come in handy if you want to impress your teacher, parents, or friends.

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## Is Magic All Math

I have met people who are under the impression that magic is all math based. This might be from an experience they had with some math tricks when they were younger. Perhaps these people have never seen good sleight of hand magic- cards, coins, rings, etc.

Magic is not math. There are some math tricks that can be very baffling and puzzling. Math tricks are in a different category than magic tricks. Math tricks give a sense of amusement. They are usually very procedural and wont blow your mind. The enjoyment of a math trick is more about working it out. After doing a math trick you want to try it and work through and figure out the math.

Students really get into it because they truly want to learn how to do it themselves. Working on these tricks is good for learning and deduction skills and a good way to get students thinking. Curiosity can lead us to embrace and apply both new and familiar concepts and skills, including algebra. These tricks can serve as an aid in learning basic math. Check out the video below to see these tricks performed.

## Is It Magic Or Is It Maths

##### Age 11 to 14Challenge Level

Here are three ‘tricks’ toamaze your friends.

But the really clever trickis explaining to them why these ‘tricks’ are maths and not magic.Like all good magicians, you should practise by trying them. Canyou explain how they work?

 This trick will impress even your maths teacher.
• Think of a number.
• Take away you original number.

Try this with a differentstarting number. Did you get a different result? Why does thishappen?Write the answer on a piece of paper without letting anybody see itand seal it in an envelope. Have somebody hold the envelope and atthe end ask them to open it and reveal the number you wrote at thebeginning. Wow, Magic!

 Guess how much money people have in their pockets!

Without giving you anyinformation, ask a friend to count the value of some coins andwrite the amount on a piece of paper. Then ask your friend to:

• Double the amount.
• Add the first odd prime number to the new total.
• Multiply the result by 1/4 of 20.
• Subtract the lowest common multiple of 2 and 3.

For the grand finale, youask for the final answer. Take off the last digit and you will beable to work out how much the coins are worth!

 Amaze your audience by working out not only their age but alsowhat size shoe they wear! Wow them even more by telling them howthe maths works. Give them the following directions but tell them not to show youany calculations:

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## Math Tricks Explainedthe Math Behind The Magic

Ever wondered how a certain math trick works? Me too! On this page you’ll get math tricks explained so you can understand the math behind the magic!

So why did I decide to write a page that takes some of the mystery out of it. Well, since this site is all about helping students enjoy and learn math, showing a student why, can sometimes motivate them to explore even more!

And besides….,knowing the magic behind the math, builds their math confidence!

So if the person you do this trick on is 12 years old, here’s how it would work:

Step 1: 1 x 5 = 5 Step 2: 5 + 3 = 8 Step 3: 8 x 2 = 16 Step 4: 16 + 2 = 18 Step 5: 18 â 6 = 12

And there you have itâ¦..the age of person is 12.

## How Does The 1089 Trick Work

Math Magic Trick part 2

The mystery is this: first, take any three digit number, where the first and last digits differ by two or more and reverse the number to produce a new one. Then subtract the smaller from the larger producing another new number. If you reverse this number and this time add the two, the result will always be 1089.

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## Inventing Your Own Tricks

You can make up tricks on your own as long as your rules allow you to:

• draw the pictures,
• use whole bags and whole marbles , and
• subtract only the marbles you can see.

Drew, age 9, kept asking for new tricks, and then started inventing tricks of his own. Here are two to practice on. Draw the pictures yourself, to figure out what the magician should predict the result will be. Then make up your own tricks.

Trick 1: words for each step Trick 1: Pictures

## How Gcse Maths Algebra Can Make You A Magician

We can prove this will always work with a bit of help from our old friend, algebra.

Say the number you chose is x.

We are now going to use GCSE algebra to work out what number we will end up with.

First, we multiply x by 3, which gives us 3xThen we add 30, which gives us 3x + 30Then we multiply by 2, which gives us 2Expanding that bracket, we get 6x + 60Then we divide by 6, which gives us ÷ 6Which when simplified, gives us x + 10Then, we subtract the original number, which was x: x + 10 xWhich leaves us with. 10.

So, this is why it does not matter what value of x you chose, because the xs always cancel out.

What this also means is that you can edit this trick with infinite possibilities.

So lets say I didnt like the number 10 and I wanted the magic number to be 12 this time. All I would need to do is change the third step.

Here, I have edited the trick so that 12 is the magic number. Adding 36 instead of 30 will lead to 12 being the end product as 36 ÷ 6 = 12.

• Pick a number.
• 56 44 = 12.

Try creating your own unique maths magic trick! The possibilities are endless! Thanks, algebra!

There are many benefits to playing mathematical games like this.

We have a series of other exercises detailed in our blog, from helping you master your multiplication tables to mind-bending games such as Kaprekars Constant.

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## Magic Trick Based On Deep Mathematics

I am interested in magic tricks whose explanation requires deep mathematics. The trick should be one that would actually appeal to a layman. An example is the following: the magician asks Alice to choose two integers between 1 and 50 and add them. Then add the largest two of the three integers at hand. Then add the largest two again. Repeat this around ten times. Alice tells the magician her final number \$n\$. The magician then tells Alice the next number. This is done by computing \$ n\$ and rounding to the nearest integer. The explanation is beyond the comprehension of a random mathematical layperson, but for a mathematician it is not very deep. Can anyone do better?

• 54Dec 26 ’09 at 0:09
• 20\$\begingroup\$I have discussed this question with Persi. He could not come up with anything significant . \$\endgroup\$Dec 26 ’09 at 16:30
• 22\$\begingroup\$I’ve also heard Persi talk about this subject, and my guess is that he would say that the requirements of “deep mathematics” and “would actually appeal to a layman” are nearly incompatible in practice.\$\endgroup\$Dec 27 ’09 at 13:54
• 11\$\begingroup\$Whenever I see this question’s title, I can hardly resist opening a complementary “Deep mathematics based on magic tricks” community wiki.\$\endgroup\$May 16 ’13 at 7:51
• 9\$\begingroup\$Isn’t it risky to do magic tricks that require a member of the audience to carry out a computation? What do you do if Alice botches the computation?\$\endgroup\$

Five unrelated items:

## Bonus Math Magic Trick

This is definitely the best trick. It involves the 4 colored tables below. If you want to do this trick you can take a screen shot of the 4 tables below. You dont know in advance what number the spectator will pick. Plus it is always different. They can think of any number between 1 and 30, it is up to your spectator. I will walk you through the procedure of the trick, unfortunately I cannot perform it for you.

• Have your spectator think of a number between 1 and 30.
• Show the cards one at a time and ask which colors have their number.
• Add the numbers at the top left corner of the cards with their number.
• This will give you their number.
• PRO TIP: Whenever giving instructions make sure you are clear and go slow. Make sure they closely look at each card so they dont miss their number. If your spectator needs glasses to see make sure they put on their glasses. Otherwise the trick can get messed up. If a spectator messes up it is the magicians fault, always remember this.

##### Matt

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