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.

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: