Problem B and Solution

Nice Flow

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.

Using the symbols below, create all possible flowcharts.

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

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 \(16\).Here are the six possible flowcharts:

Here are the two flowcharts that work: