How to Learn a Math Trick

Step-by-Step Guide

1. 1

   Step 1: Ask a friend to quietly think of a three-digit number.

   Get him or her to remember it.
   
   The only condition is that its first and last digit must be different by more than one
   - for example, 112 would not work because there is a difference of only one between the first and last digits (1 and 2). , While you, on the other hand, don't.
   
   Now tell your friend, "Reverse the number, but don't tell it too me." For Example, if he or she chose 209
   - reversing it would be
   902. , All this is done without your knowing what any of the numbers are. ,, Say, "I can guess your secret total! Its
   1089." No, no! Do not tell anyone that it's 1089 no matter what numbers they pick; you'll be right every-time! Do not do another example right then! Wait a week for forgetting, and try it on another person that may have been there before! ,, Notice that the 2nd digit of this number will always be a 9, this is because the 2nd digit of the original and reversed number are the same, therefore giving 0, and the last digit of the number you are subtracting is greater than the last digit of the number you are subtracting it from, therefore you must "borrow" from the digit before, leaving a 9 as the 2nd digit. ,, However, we still need to take into account our middle number.
   
   This is 9, so 9+9=18. , which read together gives us
   1089...
2. 2

   Step 2: Your friend

3. 3

   Step 3: will need a calculator.

4. 4

   Step 4: Now tell your friend to use the calculator to subtract the smaller number from the larger one of his or her secret pair (that's 902-209=693

5. 5

   Step 5: in this example).

6. 6

   Step 6: Tell your friend to now take the result of the subtraction (693) and reverse that (396)

7. 7

   Step 7: and then to add it and its reverse together.

8. 8

   Step 8: Your turn now.

9. 9

   Step 9: The first and last digits must have a difference greater than 1 because otherwise the following steps would produce a number which does not have 3 digits

10. 10

    Step 10: therefore it would not work;

11. 11

    Step 11: Reversing and subtracting the number gives the difference.

12. 12

    Step 12: No matter what number is chosen (so long as it fulfills the criteria)

13. 13

    Step 13: the first and last digit of the number derived from step 3 will always add together to make 9. a+b=c and 10+b-a=10-c

14. 14

    Step 14: adding these together would give us 10

15. 15

    Step 15: but as we had to "borrow" to complete our subtraction 1 has been taken from the first digit

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    Step 16: therefore decreasing the number derived from adding the digits together by 1

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    Step 17: making it 9.

18. 18

    Step 18: Because the first and last digits add together to make 9

19. 19

    Step 19: when the number is reversed and added to itself the first and last digits will be 9.

20. 20

    Step 20: This gives us 9 for our first digit

21. 21

    Step 21: 18 for out second number (I know 18 isn't a digit; I'm getting there; be patient) and 9 for our last digit

22. 22

    Step 22: however as 18 is NOT a digit the 1 must be carried into the first column

23. 23

    Step 23: therefore leaving us with 9+1

Detailed Guide

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