Finding 5-Digit Numbers w/ Neighbouring Digits Differing by 3

[thagamizer]

how many 5 digit numbers are there in which every two neighbouring digits differ by 3?

can you please tell me if i have to do this all by trial and error or is there some sort of formula i need to make to do this
thanks

 

[matt grime]

Trial and error? You mean you're going to guess a number and see if it satisfies the condition?

What if I told you the first digit were a 1? What is the second digit?

 

[thagamizer]

14741
but there's too many possibilites

 

[thagamizer]

what i meant is do i need to make a formula to work out the number of combinations

 

[matt grime]

There are not too many possibilities. And that isn't the only one that starts with 1. You could write down a recurrence relation, if you wished, but I doubt that will help - just do it, it isn't very hard, and won't take you very long.

 

[prasannapakkiam]

This was in the UNSW Maths comp. Hint: it is around 40...