Answer:
4 numbers
Step-by-step 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.
[tex]ABABA = 0B0B0[/tex]
or
[tex]ABABA = 5B5B5[/tex]
The first format [tex]ABABA = 0B0B0[/tex] cannot be considered because the number starts with 0 which means that
[tex]ABABA = B0B0[/tex] ---- This is 4 digits not 5
Taking into consideration: 5B5B5
We know that 15 is a product of 5 and 3
i.e.
[tex]15 = 5 * 3[/tex]
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.
