Math Magic - fun math for everyone
From the collection of P. Narayanan (Amazing Vijay’s father)
People love math magic - whether it is a super fast magic square or my tricky addition opening trick, I always get compliments about the math tricks. Here are a few more for your fun.
- Fun fact: Did you know that the letters "a", "b", "c" or "d" do not appear in the spelling of any number from 1 to 99?
- Here's a mathematical oddity. I am going to prove 1=2
Of course it is a fallacy. If you want to know where the fallacy is or what a fallacy is, you can send me a quick email at firstname.lastname@example.org.
The 9 principle:
- Puzzle: Write down any 3 digit number. Reverse it. Subtract the smaller number from the larger number. Now if you tell me the first or the last digit, I can tell you the other two digits of the answer. Answer: The answer will always be x9y and first and last digit will add up to 9 also. So tell them that the middle digit is 9 and then subtract from 9 to come up with the other digit
Puzzle: Write down any 3 digit number. Reverse it. Subtract the smaller number from the larger number. Now reverse the answer and add the 2 numbers together. I can tell you the answer.
Please write down say a 4 digit number. Now reverse the digits to get another random number. Now subtract the smaller number from the larger number to get yet another random number. We will stop now. Now please circle one of these digits in the final answer. Now if you read out the remaining digits (but not the one you circled) and concentrate on the number you circled, I can immediately tell you the number you circled and are concentrating on.
Answer: The final sum is a multiple of 9 and hence all the digits of this number add up to 9. As they tell you the remaining digits, just keep a running total of the digits in your head. If the total crosses 10, you can keep reducing this to a single digit by adding these digits together [this method of summing the digits is called calculating the digital root of the number]. In the end subtract your total from 9 to get the missing digit - this is the one they circled. Reveal it after suitable fanfare.Example: They think of 7362. Ask them to reverse it: they get 2637 but do not tell you. Subtract the smaller from the larger: they get 4725 but do not tell you. Now they can think of any digit e.g. 7. They rattle off the remaining digits to you - 4, 2, 5. You total these mentally to get 11 - add these two digits 1+1=2. Subtract 2 from 9 to get their digit 7 !! Pretend to read their thoughts and say they must have circled the number 7 :-)
Answer: It is always 1089.
Finding the square of any number ending with 5.
First digit x (first digit+1) and then last 2 digits are always 25
E.g 35 x 35 = 3x4 = 12, so the answer is 1225
E,g 85 x 85 = 8x9 = 72, so answer is 7225
Finding the square of any numbers starting with 5.
First 2 digits are (25+second digit) ; Last 2 digits are the square of the second digit
E.g. 56 x 56 = 25+6 = 31, so the answer is 3136.
E.g. 52 x 52 = 25+2 = 27, so the answer is 2704
Multiplying by 11.
Write down the last digit, Add 2 digits and write down answer to the left. Write first digit to left of this.
E.g. 23 x 11 = 2 [(2+3)=5] 3 ->253.
Sometimes you have to carry over – but then this may not be so quick
E.g. 98 x 11 = [(9+1 (carry))=10] [(9+8)=7(and carry 1)]  -> 1078
Looks confusing but quite easy - write last digit - 8. Now add the digits 9+8=17. Write 7 as the digit before 8 and then carry 1 and add to first digit. So 1078.
Another short cut to multiply by 11 is to first multiply by 10 and add the number to that. So look at the number, add a zero to the end and then add the number to this. E.g. 86x11 = 860+86 = 946.
Can you remember the number 142857. This is a very interesting number and the digits can be cyclical and they repeat indefinitely. Using this number, any division by 7 can be easy.
E.g. 1/7 = 0.142857142857142...
and 2/7 = 0.2857142857142857..... or 28.57%
and 6/7 = 0.85714285714285.... or 85.7%
All you have to do is figure out the first digit and then just write down the remaining digits which will always be cyclical and the digits 142857 in circular order.
- Do you like Magic Squares. In fact, I am really fond of them and sometimes perform an instant magic square demonstration at my magic show. Here's a magic square that adds up to 62. Anyway you add the numbers, you will get 62. There are over 30 ways to add numbers to get 62 !! Rows, diagnals, Columns, smaller 4 square totals, corners, middle squares, etc. etc.
Visit www.amazingvijay.com often and Click on Math Puzzles.
If you like them, send an email to email@example.com
Online Magic Tricks for magicians
Here are some magic tricks that you can try on your friends and co-workers. I wrote these using Adobe Flash CS4. Sorry, you need to know the secret. So you must send me an email if you want to know how to do these tricks.