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Problem of the Week
Problem A
Follow the Rules

Consider the following step-by-step instructions:

  1. Pick a \(2\)-digit number.

  2. If the number is even, divide it by \(2\). If the number is odd, add \(10\) to the number.

  3. If the result of the calculation in step \(2\) is a \(2\)-digit number, add its tens digit to its ones digit. Otherwise, add \(20\) to the number calculated in step \(2\).

  4. If the result of the calculation in step \(3\) is a multiple of \(5\), divide it by \(5\). Otherwise, add \(12\) to the number calculated in step \(3\).

  5. If the result of the calculation in step \(4\) is greater than \(30\), add \(1\) to it. Otherwise, subtract \(1\) from the number calculated in step \(4\).

  1. What is the result of following these instructions if you start with \(25\)?

  2. What is the result of following these instructions if you start with \(95\)?

  3. What is the result of following these instructions if you start with \(16\)?


Themes: Computational Thinking, Number Sense