Question

A thief entered an orange garden guarded by 3 guards and stole some oranges. The first guard caught him. To get rid of him, the thief gave him half of the stolen oranges and two more. Then the second guard came upon him; to escape he gave him half of the oranges he had with him plus two more oranges. Near the exit he came across the third guard; and he gave him half of the oranges and two more oranges. Once escaped, he saw that he had only one more orange. How many oranges had the thief stolen

Answer 1

Let's assume that the thief originally stole X oranges from the garden.

When the thief gave half of the oranges and two more to the first guard, he was left with (X/2 - 2) oranges.

When the thief gave half of his remaining oranges and two more to the second guard, he was left with ((X/2 - 2)/2 - 2) oranges.

When the thief gave half of his remaining oranges and two more to the third guard, he was left with (((X/2 - 2)/2 - 2)/2 - 2) oranges.

We are also given that the thief had only one orange left after giving oranges to the third guard. Therefore:

(((X/2 - 2)/2 - 2)/2 - 2) = 1

Simplifying this equation, we get:

(X/8) - 1 = 1

(X/8) = 2

X = 16

Therefore, the thief had stolen 16 oranges from the garden.