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?
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?