Question

A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy numbers are divisible by 15?

Answer 1

4 numbers

Explanation:

Given

Five Digit Flippy Numbers

Required

Determine the number of these digits divisible by 15

Represent the format of this digits as: ABABA

A number is divisible by 15 if and only if it ends with 5 or 0

i.e.

`ABABA = 0B0B0`

or

`ABABA = 5B5B5`

The first format
`ABABA = 0B0B0` cannot be considered because the number starts with 0 which means that

`ABABA = B0B0` ---- This is 4 digits not 5

Taking into consideration: 5B5B5

We know that 15 is a product of 5 and 3

i.e.

`15 = 5 * 3`

5B5B5 is divisible by 5 because it ends with 5. So, for a number of this format to be divisible by 15, it must be divisible by 3

Numbers in this category are: 50505, 53535, 56565 and 59595

Hence, there are 4 five-digit flippy numbers divisible by 5.