Answer
$36$ plants.
Work Step by Step
Step 1. Assume the thief steals $x$ number of plants, when the thief meets the first guard, he needs to give away $\frac{x}{2}+2$ plants, leaving him with $y_1=x-(\frac{x}{2}+2)=\frac{x}{2}-2$ plants.
Step 2. When he meets the second guard, he needs to give away $\frac{y_1}{2}+2$ plants, leaving him with $y_2=y_1-(\frac{y_1}{2}+2)=\frac{y_1}{2}-2==\frac{x}{4}-1-2=\frac{x}{4}-3$ plants.
Step 3. When he meets the third guard, he needs to give away $\frac{y_2}{2}+2$ plants, leaving him with $y_3=y_2-(\frac{y_2}{2}+2)=\frac{y_2}{2}-2=\frac{x}{8}-\frac{3}{2}-2=\frac{x}{8}-\frac{7}{2}$ plants.
Step 4. Given $y_3=1$ in the Exercise, we have $\frac{x}{8}-\frac{7}{2}=1$ which gives $x=8\times\frac{9}{2}=36$ plants.
