Try this beautiful Problem based on Divisibility Rule from Math Kangaroo (Benjamin) 2020.
We say that a three-digit number is balanced if the middle digit is the arithmetic mean of the other two digits. How many balanced numbers are divisible by 18 ?
Arithmetic
Divisibility Rule
Arithmetic Mean
Algebra by Gelfand
Math Kangaroo (Benjamin), 2020
6
Let the number be 
By the given condition of arithmetic mean we get,
![\[\frac{a+c}{2}=b\]](https://www.cheenta.com/wp-content/ql-cache/quicklatex.com-9a35d337fa82cf6a86f1d24810091257_l3.png "Rendered by QuickLaTeX.com")
Now from here can I conclude 
are of the same parity?
Given that the number is divisible by 
Given number must be divisible by both 
and 
.
Apply divisibility rule of to guess the values of 
.
Here the values of 
are 
.
the values of 
are 
.
Now guess the values of 
?
And then find the possible pair of 
?
The possible values of are 
, 
, 
, 
, 
, 
.
So, how many possible numbers are there?
Try this beautiful Problem based on Divisibility Rule from Math Kangaroo (Benjamin) 2020.
We say that a three-digit number is balanced if the middle digit is the arithmetic mean of the other two digits. How many balanced numbers are divisible by 18 ?
Arithmetic
Divisibility Rule
Arithmetic Mean
Algebra by Gelfand
Math Kangaroo (Benjamin), 2020
6
Let the number be
By the given condition of arithmetic mean we get,
Now from here can I conclude are of the same parity?
Given that the number is divisible by
Given number must be divisible by both and .
Apply divisibility rule of to guess the values of .
Here the values of are .
the values of are .
Now guess the values of ?
And then find the possible pair of ?
The possible values of are , , , , , .
So, how many possible numbers are there?
