'Robust' number
Source: Brazil National Olympiad 2019 - level 2 - #1
November 23, 2019
Brazilian Math OlympiadDigitsnumber theory
Problem Statement
An eight-digit number is said to be 'robust' if it meets both of the following conditions:
(i) None of its digits is .
(ii) The difference between two consecutive digits is or .Answer the following questions: (a) How many are robust numbers?
(b) A robust number is said to be 'super robust' if all of its digits are distinct. Calculate the sum of all
the super robust numbers.