Answer
36
Work Step by Step
Assume that the thief has stolen Aplants.
After giving one-half of what he has and 2 more plants to first guard, he has \[B\]plants with him.
And after giving to the second guard one-half of remaining and 2 more, he has C plants.
And after giving to the third guard, he has D plants with him.
Express it in algebraic format to obtain,
\[\begin{align}
& A-\left[ \frac{1}{2}A+2 \right]=B \\
& B-\left[ \frac{1}{2}B+2 \right]=C \\
& C-\left[ \frac{1}{2}C+2 \right]=D \\
\end{align}\]
It is provided that at last he has 1 plant with him so, value of Dis 1, now put the value of D in last equation and solving it further we get all values.
\[\begin{align}
& C-\left[ \frac{1}{2}C+2 \right]=1 \\
& \frac{C}{2}-2=1 \\
& \frac{C}{2}=3 \\
& C=6
\end{align}\]
Now substitute back 6 for C in the second equation and solve for B.
\[\begin{align}
& B-\left[ \frac{1}{2}B+2 \right]=6 \\
& \frac{B}{2}-2=6 \\
& \frac{B}{2}=8 \\
& B=16
\end{align}\]
Finally, substitute back 16 for B in the second equation and solve for A.
\[\begin{align}
& A-\left[ \frac{1}{2}A+2 \right]=16 \\
& \frac{A}{2}-2=16 \\
& \frac{A}{2}=18 \\
& A=36
\end{align}\]
So, here the number of plants the thief stole was 36.
The thief stole 36 plants.
