Problem of the Week
Problem B and Solution
Nice Flow

Problem

1. For each flowchart below, determine the output value when the number \(13\) is the input number and when the number \(10\) is the input number.

   

   Hide/Reveal Description of flowcharts

   The flowchart on the left has the following steps, in order.

   1. Input a number

   2. Multiply by \(6\)

   3. Subtract \(2\)

   4. Divide by \(2\)

   5. Output the number

   The flowchart on the right has the following steps, which include answering a yes or no question.

   1. Input a number

   2. Add \(3\)

   3. Is the sum greater than 14?

      1. If YES, then output the number.

      2. If NO, then return to Step 2.

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2. Using the symbols below, create all possible flowcharts.

   

3. Which of the flowcharts in part (b) give an output of \(248\) for an input of \(35\)?

Solution

1. For the flowchart on the left:

   When we input \(13\), we first multiply by \(6\) to get \(78\).
   Then, we subtract \(2\) to get \(76\).
   Finally, we divide \(76\) by \(2\) to get \(38\).
   Thus, the output is \(38\).

   When we input \(10\), we first multiply by \(6\) to get \(60\).
   Then, we subtract \(2\) to get \(58\).
   Finally, we divide \(58\) by \(2\) to get \(29\).
   Thus, the output is \(29\).

   For the flowchart on the right:

   When we input \(13\), we first add \(3\) to get \(16\).
   Since \(16>14\), the output is \(16\).

   When we input \(10\), we first add \(3\) to get \(13\).
   Since \(13\) is not greater than \(14\), we add \(3\) again to get \(16\).
   Since \(16>14\), the output is \(16\).

2. Here are the six possible flowcharts:

   

3. Here are the two flowcharts that work: