Wednesday 22 December 2010

The 1089 Trick

Write down a 3 digit number whose numbers are decreasing

Then reverse the digit to create a new number, and subtract this number  from the original number.

With the resulting number, add it to the reverse to itself.

The number you will get 1089

This works by:

Represent the number with ABC

Represent this to get CBA

A is hundreds B is Tens C is Units

Hundreds  Tens    Units 
   A               B         C  
-  C               B         A

Subtract 1 hundred, and add 9 tens and 10 Ones (-100, +90, +10 = 0, so the answer won't change). To the number ABC we wont make any difference (as we are adding 100 and taking 100 away, This just lets us specify that C had to be bigger than A).

Hundreds  Tens    Units 
   A               B         C  
-  C               B         A 
-  1
+                   9        10

(A-1-C)         9       (10+C-A)

Reverse the answer and add the two numbers together.

A-1-C        9       10+C-A

     A-1-C      9    10+C-A 
+  10+C-A    9     A-1-C 
 ---------------------------
      9            18       9

(Simplify:)

    10        8        9

No comments:

Post a Comment