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

ig there are 4 five-digit flippy numbers divisble by 15.

The possible numbers are; 50505, 53535, 56565, 59595.

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Answer 2

Answer:

The possible flippy numbers are :  $50505, 53535, 56565, 59595$.

Step-by-step explanation:

We need $5$ digit flippy numbers which are divisible by $15$.

For a number to be divisible by $15$, it has to be divisible by $3$ and $5$.

For a number to be divisible by $5$, it's last digit has to be $0$ or $5$.

Since it is a flippy digit and $0$ cannot start the number as it is a five digit number, then the first and last digits must be $5$.

Also, the center digit must be $0$ or $5$ to fulfill both conditions.

Thus, the number should be in the format :

      $5N5N5$

For it to be divisible by $3$ :

since $5 + 5 + 5 = 15$ is divisible by $3$, the $N + N$ can be equal to $0, 6, 12,$ or $18$ since $N$ is identical.

Thus, possible numbers are : $50505, 53535, 56565, 59595$.