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A positive integer is written on a blackboard. At each step, we are replacing the number on the board with the sum of its digits. Obviously, the number will get smaller and smaller at every step until it has only one digit and it will be constant after that. For example if we start with 298799034 on the blackboard, then it will continue like 298799034 51-6-6-6-... If we begin with 3152022 +14 written on the blackboard, then what is the single digit number we will eventually reach?

A positive integer is written on a blackboard. At each step, we are replacing the number on the board with the sum of its digits. Obviously, the number will get smaller and smaller at every step until it has only one digit and it will be constant after that. For example if we start with 298799034 on the blackboard, then it will continue like 298799034 51-6-6-6-... If we begin with 3152022 +14 written on the blackboard, then what is the single digit number we will eventually reach?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A positive integer is written on a blackboard. At each step, we are replacing the number on the board with the sum of its digits. Obviously, the number will get smaller and smaller at every step until it has only one digit and it will be constant after that. For example if we start with 298799034 on the blackboard, then it will continue like 298799034516-6-6-... If we begin with 3152022 +14 written on the blackboard, then what is the single digit number we will eventually reach?
Transcribed Image Text:A positive integer is written on a blackboard. At each step, we are replacing the number on the board with the sum of its digits. Obviously, the number will get smaller and smaller at every step until it has only one digit and it will be constant after that. For example if we start with 298799034 on the blackboard, then it will continue like 298799034516-6-6-... If we begin with 3152022 +14 written on the blackboard, then what is the single digit number we will eventually reach?
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