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?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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