‘Flash Anzan’ and Can You Answer this Simple Addition Puzzle?

Today, there is a puzzle of sorts but the crux of this post are the videos at the bottom of the page showing superhuman feats of addition that will make you gasp!

Add up the following numbers quickly and in your head:

One thousand

Forty

One thousand

Thirty

One thousand

Twenty

One thousand

Ten

Scroll down for the answer and for remarkable videos showing superhuman powers of addition.

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Answer: 4,100.

Many people when given this puzzle answer 5,000. They reach the penultimate step and reach 4,090 then add 10 and mistakenly reach 5,000. This addition problem is best presented verbally to a friend.

The below video features the Japanese champion at adding up numbers:

 

The below video features two Japanese 9 year old children playing a word game whilst they add up 30 numbers flashed on a screen in 20 seconds.

 

In Japan every year, over 1 million students learn to use a type of abacus, known in Japan as a soroban. The Japanese students become so familiar with using the abacus that they can use their fingers and a mental image of the abacus to answer the addition questions without the actual physical abacus. ‘Flash Anzan’ involves 15 3-digit numbers being flashed up on a screen and the problem lies in adding them up. The amount of time they appear on the screen for is remarkably small, so much so that in some cases a person unfamiliar with ‘Flash Anzan’ can’t recognise the numbers. The below video shows 15 numbers being flashed on a screen in 1.85 seconds. The world record holder at the time correctly answered this sum (and indeed went faster). Interestingly, those performing Flash Anzan can’t remember the numbers on the screen or the progressive sum of the numbers on the screen, only the final answer.

An Amazing Magic Trick That Requires No Skill

You borrow a friend’s iphone and open up their calculator app. You ask them to type in their year of birth and hit multiply, you ask them to type a number between 1 and 100 and hit multiply, you ask them to type the number of chocolates they’ve eaten in their life and hit multiply and finally you ask them to type a random number between 300 and 400 and hit equals. A 10 digit random answer appears on their phone. You ask your friend to reach into their pocket and they find a folded up piece of paper. They unfold it and the number that has been in their pocket the entire time matches exactly the answer to these seemingly random numbers multiplied together. There’s more! You ask them to phone the random number and your phone begins to ring: it’s your phone number!

I have spent a small fortune on magic tricks over the years but this free trick requires no skill, props or money (other than the presence of a certain type of phone or calculator).

The method: This trick relies on a mathematical principle that numbers multiplied by 0 equal 0; in essence it’s a maths trick. The trick works on iphones and certain calculators. Firstly, open the iphone calculator app. Type your phone number into the calculator and multiply it by 1 (hit x and 1 on the keypad). Now, add 0 and multiply (hit + then 0 then x). The final step is to rotate the phone 90 degrees so it turns to landscape mode (this should open up more options on the calculator. In landscape mode, hit open bracket (this symbols “(” should appear as the first symbol of the top row). Rotate the phone back to its normal portrait mode and the trick is ready. This entire trick relies on what is known as the toxic force.

In summary,

Type in your phone number

x 1

+ 0

x

Rotate the phone 90 degrees and press (

Rotate the phone back to portrait mode.

The above preparation can be done before the trick begins or quickly on a friend’s borrowed phone under the guise of trying to find the calculator app. Before the trick begins, you also need to hide your phone number somewhere in the room away from where you are sitting.

Ask your friend to type random numbers into the phone and hit multiply after each number. Some ideas of questions to generate these numbers appear at the top of this article. After several numbers, ask your friend to hit equals and your phone number will appear on their phone as the answer! There are several variants to this trick but I find that it’s great impromptu magic that generates amazed reactions.

 

 

 

A Calculator Maths Puzzle and Trick

I ask Gemma to press random single digits on her calculator and multiply them together one-by-one while my back is turned (for instance 3x6x8x2x7x3x5). I tell her to continue this process until she has produced an answer that is between 7 and 11 digits long. I tell her to choose one digit from the answer that she must keep a secret. The remaining digits she can read back to me in any order, randomly. She reads back “0, 4, 1, 6, 9, 3”. What is the secret digit that Gemma is almost certainly thinking of?

Scroll down for a clue and further down for the answer and to learn this trick.

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Clue: This trick will almost always work using the method described in the question. To guarantee it working, sometimes I will say “multiply random number on the calculator like this…” and I will press 6 x 3 x and the other person will continue this process that I have started.

Scroll down for the answer and the method.

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Answer: The secret digit that Gemma was thinking of in this question was a “4”.

The Method: This trick relies on a trait of multiplying the number 9 by other numbers and adding up digits of the answer that will always be a multiple of 9. For instance, if I multiply 9 x 3 x 7 the answer is 189. If I add the digits of the answer up, they equal 18 which is a multiple of 9.

The trick process involves adding the digits up the other person reads out until you end up with an answer. You then add the digits up of your answer until you have a single digit. The final step is to work out 9 minus this single digit and this answer will be the person’s secret number.

Using this method, it’s possible to determine the number someone is thinking of. For example, if someone multiplies 9 x 3 x 4 x 8 x 7, they will see the answer on their calculator as ‘6048’. I ask them to choose a secret digit of their answer to not reveal (say they choose 8) and I ask them to read back the remaining digits in any order. They say “6, 4, 0”. In order for me to determine their secret digit, I add up in my head 6 + 4 + 0 which equals 10. I then add up the two digits of my answer 1 + 0  which equals 1. 9 minus 1= 8 therefore 8 is the secret digit.

In the question at the start of this post, Gemma read back the digits “0, 4, 1, 6, 9, 3” whilst remembering a secret number. To work out her secret number, you needed to add these digits together. They equal 23. 2 + 3 = 5. 9 minus 5 = 4 therefore 4 is the secret number.

To summarise the method for this trick; to determine the secret number, add up the digits read out to you. Following this, add up the digits of the answer so you end up with a single digit. Finally, work out 9 minus this single digit and this is the person’s thought of secret number.

There are some caveats to this trick. It isn’t a certainty that the person pressing the numbers into the calculator at the start of the trick will press 9. Most of the time they will but there are some other number combinations that they may press that will still make the trick work, for instance if they press the digit 3 twice or 6 and 3.

To guarantee this trick working, I sometimes show the person what I mean when I ask them to multiply random digits into the calculator and I will start things off for them by pressing 6 x 3 x ….. and they will keep pressing digits whilst my back is turned. If this sure-fire version of the trick is used, then they don’t have to be restricted to pressing single digits and can multiply any numbers they would like.

This maths trick is fun to present as magic under the guise of reading the person’s mind.

 

How To Work Out Cubed Roots In Your Head

Learn how to appear like a maths whiz with this cool trick to work out cubed roots in your head. For instance if someone asks you what is the cubed root of 175,616 is, you can immediately answer “56.”

This trick works by asking a spectator to secretly type into a calculator a two digit number. The spectator is then asked to hit multiply and type the same two digit number again, multiply and type the same two digit number again and finally, equals. In essence someone has cubed a two digit number. They read the answer out to you and using a technique that I will outline, you can announce the answer.

The technique:

Working out the first digit of the answer.

A tiny amount of memorisation is required. You must remember the cubes of the numbers from 1 to 9. These are outlined below:

1 cubed=1

2 cubed=8

3 cubed=27

4 cubed=64

5 cubed=125

6 cubed=216

7 cubed=343

8 cubed=512

9 cubed=729

The numbers in the right hand column above relate to the thousands part of the answer the spectator gives you. For instance, if the spectator’s answer for cubing a number is 262,144, you focus on the 262 part of the number as this is the thousands part of the number. In the above chart’s right hand column, you place where this number (262) belongs. It is bigger than 6 cubed (216) and smaller than 7 cubed (343) so we know that cubed number the spectator is thinking of is between 60 and 70.

Working out the 2nd digit of the answer.

Working out the second digit of the answer is much simpler. You just focus on the very last digit of the answer the spectator reads you, for instance if their cubed answer is 262,144 then you focus only on the last digit which is 4.

If the last digit the spectator reads is:

1 then the second digit of the answer is…1

2 then the second digit of the answer is…8

3 then the second digit of the answer is…7

4 then the second digit of the answer is…4

5 then the second digit of the answer is…5

6 then the second digit of the answer is…6

7 then the second digit of the answer is…3

8 then the second digit of the answer is…2

9 then the second digit of the answer is…9

0 then the second digit of the answer is…0

The above chart can be condensed into: whatever the last digit the spectator reads is the same last digit in your answer- except if they read 3 or 7: these numbers switch and except if they read 8 or 2: these numbers switch.

Examples

If the spectator reads out 493,039 then we look at what the thousand number is, in this case 493. In the first chart 493 is between 7 cubed and 8 cubed therefore we know the first digit of our answer is 7. To work out the second digit of our answer, we look at the last digit read by the spectatator in 493,039 which was a 9 therefore as we know the last digit stays the same unless its a 2,3,7 or 8 then we know the last digit in our answer is a 9. We therefore announce 79 as the cubed root of 493,039.

Another example: If the spectator reads 110,592 as the cubed number, we immediately work out what the thousands part of the number is, in this case 110. Based on the top chart, 110 falls in between 4 cubed and 5 cubed, which means we know the answer starts with a 4. The last digit the spectator read out was 2 and we know 2 and 8 change places for the last digit so the answer is 48.

Different steps are necessary when you work out these answers in your head. I will give one last example of how I work out the answer when given a cube. If someone reads out 658,503 then I think 658 is quite a big number so I try and recall what 7 cubed, 8 cubed, or 9 cubed is. I remember 7 cubed as 343, 8 cubed as 512 and 9 cubed as 729 and I determine that 658 is between 8 cubed and 9 cubed. I then announce the answer as eighty…. (and while stating the answer), I focus on the last number the spectator read which was 3 and I know 3 and 7 switch places so I announce “eighty-seven.”