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Chapter 0: Problem 70

A thief steals a number of rare plants from a nursery. On the way out, the thief meets three security guards, one after another. To each security guard, the thief is forced to give one-half the plants that he still has, plus 2 more. Finally, the thief leaves the nursery with 1 lone palm. How many plants were originally stolen?

Short Answer

Expert verified
The thief originally stole 36 plants.

Step by step solution

01

Identifying the reverse steps

Based on the problem, we know that the theif ends up with one plant. Reverse steps should be: adding 2 plants which were given to the last guard and doubling the total count to get the number of plants before encountering the last guard.
02

Applying the reverse steps for all the guards

To get the number of plants the thief had before meeting the first guard, apply the steps identified in the previous step three times, since he met three guards:\n\n- After the last guard: The thief had 1 plant. Reverse the last guard鈥檚 action by adding the 2 plants and doubling: \(2*(1+2) = 6\) plants.\n\n- After the second guard: Reverse by adding 2 and doubling: \(2*(6+2) = 16\) plants.\n\n- After the first guard: Again, reverse by adding 2 and doubling: \(2*(16+2) = 36\) plants.
03

Conclusion

Therefore, the thief originally stole 36 plants from the nursery. This is obtained by reversing the process in which the thief loses plants while meeting the guards.

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