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Explore the Back-StoryTry 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 ?

- 2
- 3
- 6
- 9
- 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 ?

- 2
- 3
- 6
- 9
- 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?

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