Math is Fun
Bookmark Add to favorites
link Link here
Math is Fun HomeHome

Math Menu
Numbers
Algebra
Geometry
Data
Measure
Puzzles
Puzzles & Quizzes
Dictionary
Illustrated Math Dictionary
Other Bits
Subject Index
Contact Us
About Us
Privacy Statement

Cite this page
Contribute item



Top-rated teacher Web sites rated by teacher usage
Edunet site of the week January 2001
Maths Is Fun is ICRA Registered

Copyright © 2009
MathsIsFun.com

Why is it always 1089

(This is the reasoning behind Always End With 1089)

 

You will need a little bit of algebra.
But stick with it, it is not difficult.
Represent the number with ABC
Reverse this to get CBA
Remember that A is Hundreds B is tens and C is units
Take CBA from ABC like this
Hundreds Tens Units
A B C
C B A
Now here is the trick: subtract 1 Hundred, and add 9 Tens and 10 Ones (-100, +90, +10 = 0, so won't change answer):

Hundreds Tens Units
A-1B+9 C+10
C B A
A-1-C 9 10+C-A
Last Step: Reverse the answer and add the two numbers together.

A-1-C 9 10+C-A
+
10+C-A 9 A-1-C
9 18 9
(simplify:)
10 8 9

As predicted the answer was 1089

Always End With 1089 Puzzles Index