Are you a school going boy/ girl who loves to have some fun with Mathematics? Are you a parent who want to teach addition to your son / daughter combined with fun? Here is a very interesting “Magic with Mathematics” that you can play with friends and children and make them wonderstruck with your wizardry.
Let me give an example of adding 5 numbers. The numbers could be anywhere from two digits to any number of digits, depending on the age of the children and their patience to do the summing.
You will start the game saying, “We are now going to do a 5-number addition; You will give the first two numbers and the 4th number; I will contribute the 3rd and 5th number. The moment you give the first number, I will give the answer of the SUM immediately, before putting the rest of the 4 numbers. Once we are finished, you can check the total and you will find my answer given at the beginning to be cent percent correct!”
Let us say, you are going to add 3-digit numbers. Ask your friend to give the first number.
Your friend says (for example): “345”.
Now you write the answer as a 4 digit number, always starting with 2 and the remaining 3 numbers equal to “Given number MINUS 2”.
In our example, you answer should be 2343 (i.e., it starts with 2 and 345-2 = 343; thus 2343).
Now ask your friend to give the second number: Let it be, say, 568.
Now YOU have to write the 3rd number. How do you do it? Subtract each digit of the above number from 9 and write it. i.e your entry shall be (9-5=4)(9-6=3)(9-8=1) = 431.
Now ask your friend to give the 4th number. Let it be, say 732. Now you write the 5th number in the same way, by subtracting each number from 9. i.e. your entry shall be (9-7=2)(9-3=6)(9-2=7)=267.
Now ask your friend to total up the five numbers. (345+568+431+732+267). Lo and behold! He will get the same answer (2343) given by you at the beginning!
For children at age group below about 12, this could really be flabbergasting.
You can try this out with any number of digits of 5-number addition. Suppose you are going to try a 6 digit number and the first number is 345651 then the sum will be a 7 digit number starting with 2 and subtracting two with the rest: 2345649. The 3rd and 5th numbers have to be put by you as usual subtracting each previous
number from 9 as explained.
Important: If you are adding, say, six digit numbers, the input numbers should be 6-digits or less and not more.
Elder children may be curious to decipher the logic behind it. Can you try to figure out the simple logic behind this magic addition?
Please try yourself. If you can't get it, read on.
Consider the 2nd and 3rd number as one pair and also 4th and 5th number as another pair. What you are doing in effect while writing the 3rd and 5th number is to make sum of each pair to 999 (in our 3-digit sum example). That means, what ever we are doing after getting the first number is to add 999+999. This is nothing but adding 2000 minus 2. THIS IS WHAT WE PRCISELY DO WHILE WRITING THE ANSWER : We add 2 at the front (amounting to 2000) and subtract two from the rest!
You can extend this sum to 7 number addition (add 3 at front and subtract 3 on the first number to get the answer) , 9 number addition (4 and minus 4) and so on.
Simple Mathe”magic” with a secretive hidden logic!
