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Interesting Math Tricks: The Guessing Number Trick

The Guessing Number Trick |
I will share some interesting math tricks which I have learned from various sources.

1) The Guessing Number Trick

This can be used to show your mind powers!
a) Think of a 3- digit number (its first and last digits should not be same).Ex:131 should not be chosen but 132 can.
b) Reverse the number(If you chose 132 ,you get 231).
c)Find the difference between the two ( the result should be positive) and make the number have 3 digits(if it has 2 digits add a leading zero).i.e 132–231=99,make it 099. Call this number X
d)Reverse X and add it to X.
e)You can always guess the number.

The solution will always be 1089.

Let the number be abc i.e 100a +10b +c. Reversed number is cba i.e 100c+10b+a
On subtracting you get 100(a-c) +(c-a) =99(c-a) or 99(a-c) depending on which a or c is a bigger digit.Note:a not equal to c is important here.
Now the only possibilities are 099,198,297,396,495,594,693,792,891,990.
On reversing,the numbers are 990,891,792,693,594,495,396,297,198,099.

On adding each pair you always get 1089.

I love this trick because it always gives the same answer irrespective of what number the person thinks.

The Guessing Number Trick

2)The guessing Number Trick 2

This involves a lesser known Indian Mathematician Kaprekar.
  • Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)
  • Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.
  • Subtract the smaller number from the bigger number.
  • Go back to step 2.
  • Keep repeating the above process, until you get the same number twice in a row.
The answer will always be 6174 (known as Kaprekar’s constant). It also takes a maximum of 7 steps to reach 6174.

3) Magical Birthday Calculator Math Trick

Here is how you can guess anyone's birthday. Give your friend the following instructions:
  • Enter the number 7
  • Multiply by the day of your birth
  • Subtract 1
  • Multiply by 13
  • Add the month of your birth
  • Add 3
  • Multiply by 11
  • Subtract the day of your birth
  • Subtract the month of your birth
  • Tell me the result

Then, mentally, do these steps:
Divide by 10
Add 11
Divide by 100

Amazingly, your friend's birthday will appear in the result!

For example, let's suppose your friend was born on February 29. Below, I repeat the sequence of instructions, showing the result at each step in brackets.
Enter the number 7 (7)
Multiply by the day of your birth (7x29=203)
Subtract 1 (203-1=202)
Multiply by 13 (202x13=2626)
Add the month of your birth (2626+2=2628)
Add 3 (2628+3=2631)
Multiply by 11 (2631x11=28941)
Subtract the day of your birth (28941-29=28912)
Subtract the month of your birth (28912-2=28910)
Divide by 10 (28910/10=2891)
Add 11 (2891+11=2902)
Divide by 100 (2902/100 = 29.02)

The result is clear - February 29th.

4) Adding Time

Here is a nice simple way to add hours and minutes together.
Let's add 1 hr 35 minutes and 3 hr 55 minutes together.

What you do is this:
Make the 1 hr 35 minutes into one number, which will give us 135 and do the same for the other number, 3 hours 55 minutes, giving us 355.
Now you want to add these two numbers together:


So we now have a sub-total of 490.

What you need to do to this and all sub-totals is add the time constant of 40.
No matter what the hours and minutes are, just add the 40 time constant to the sub-total.

490 + 40 = 530

So we can now see that our answer is 5 hours and 30 minutes!

5) Guessing Number: Trick Yeshiva students 

This trick used to in order to amuse themselves, as a way “to find a person’s age through logic”, though the trick can work for any number.

Here’s how it goes:

You ask someone to choose a number between 1 and 100. You then ask them to divide the number into 3 and give you the remainder (e.g. if the number was 10, 9 divides neatly into three and then the remainder is 1). You then ask them to divide their original number into 5 and give you the remainder of that, and then do the same with 7.
You should now have 3 numbers, the remainders of dividing the original number into 3, 5 and 7; let’s call them x3, x5 and x7 respectively. Multiply these numbers as follows: x3 should be multiplied by 70, x5 by 21 and x7 by 15. Add them all up and if it adds up to more than 100 (technically, 105) subtract 105 until you get the right number.

An example: Let’s take the number 32.

x3 = (32 % 3) = 2
x5 = (32 % 5) = 2
x7 = (32 % 7) = 4

so now let’s multiply them:

x3 * 70 = 140
x5 * 21 = 42
x7 * 15 = 60

Adding them up we get:

140 + 42 + 60 = 242

Subtracting 105 we get 137, still more than 105, so we subtract 105 again and get 32, our original number!

This trick can work for numbers larger than 100 as well but you have to know in which group of 100 (technically 105) the original number is in. In the case of larger numbers you might have to ADD 105 instead of subtracting in order to get to the right number.

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