Question 5
(a) In a sequence of positive integers, each term after the first term is the sum of its preceding term and the largest digit of that term. What is the largest possible number of successive odd terms in such a sequence? (3 Marks)
(b) In the following sequence $\{00,01,02,03,\ldots,39\}$, the terms were rearranged so that each term after the first is obtained from the preceding one by increasing or decreasing one of its digits by 1. For example, 29 can be followed by 19, 39 or 28, but not by 30 or 20. What is the largest number of terms that can remain in their original places? (3 Marks)
(b) In the following sequence $\{00,01,02,03,\ldots,39\}$, the terms were rearranged so that each term after the first is obtained from the preceding one by increasing or decreasing one of its digits by 1. For example, 29 can be followed by 19, 39 or 28, but not by 30 or 20. What is the largest number of terms that can remain in their original places? (3 Marks)