Mental Arithmetic Magic Tricks to Amaze Others

While putting together a divisibility section for my web site that deals with mental arithmetic exercises, I came across some interesting facts about numbers that, to someone who does not understand these things, would seem like mental arithmetic magic.

In case you dont know, the divisibility of a number refers to whether a number can be evenly divided by another. For example, 24 is divisible by 2 but 13 is not as it leaves a remainder.

Here are some mental arithmetic magic tricks I have found that you can use to surprise your friends.

1. if a number is divisible by 3 then so are the numbers based on shuffling the digits of the original number. For example, consider 123 which can be evenly divided by by 3. Then 132, 213, 231, 312 and 321 (which are obtained by shuffling the digits 1, 2 and 3 that make up 123) are all divisible by 3. This is called a permutation of the digits of a number. See for yourself!

2. to make up a number that can be evenly divided by 4, make up a number and tag on the end any 2 digit number divisible by 4. For example, I make up the number 111111111, and now I tag 16 (which is divisible by 4) on the end to get 11111111116. This number can be evenly divided by 4. See for yourself!

An interesting trick follows on from this one. The following numbers are all divisible by 4: 316, 3316, 33316, 333316, and so on . . . Not what you would expect!

3. if a number can be evenly divided by 6, then any shuffle of its digits will give you a new number divisible by 6 as long as the last digit is even. For example, 1272 is divisible by 6. Permutations of its digits while keeping the last digit even gives me 2172, 2712, 1722, 7122, 7212 which are all divisible by 6. Check it for yourself!

4. to make up a number that can be evenly divided by 8, the process is very much like point 2. above. Make up a number and tag on the end any 3 digit number divisible by 8. For example, I make up the number 777777, and now I tag 016 (which is divisible by 8) on the end to get 777777016. This number is divisible by 8. Check it it for yourself!

Another interesting trick follows on from this one. The following numbers are all divisible by 8: 7016, 77016, 777016, and so on . . . Again, not what you would expect!

5. if a number can be evenly divided by 9 then so are the numbers based on shuffling the digits of the original number. For example, consider 189 which is divisible by 9. Then so are 198, 819, 891, 918 and 981. Check it it for yourself!

6. if a number is divisible by 11, then swapping its odd digits and/or its even digits will give you a new number also divisible by 11. For example, consider 154 which is divisible by 11. Then so is 451 (obtained by swapping its first and third digits). Another example, consider 1122 which is divisible by 11. Then so is 1221 (obtained by swapping its second and fourth digits). Check it it for yourself!

7. if a number can be evenly divided by 12, then any shuffling of its digits (except for the last 2) will give you new numbers also divisible by 12. For example, 14652 is divisible by 12. Then so are 16452, 41652, 46152, 61452 and 64152. Check it it for yourself!

You have to agree that such tricks do look like arithmetic magic which you can do in your head. In case you are wondering how it works. The trick lies in how we determine whether a number is divisible by another.

Feel free to join my web site to understand how these tricks work. Membership is totally free.

I, Serge M Botans, am the big chief of a web site that provides mental arithmetic exercises to those who want to regularly exercise their brain. I have also 13 years experience teaching Maths, Science and Physics.

Find practical recommendations about marketing – give a look to this publication.