Answer: Option B
The thief stole 36 diamonds. Solution:-
Let’s assume that the thief stole $x$ diamonds from the store.
When he encountered the first guard, he gave him half of his diamonds and two more, so he was left with $(x/2) - 2$ diamonds.
When he encountered the second guard, he gave him half of his remaining diamonds and two more, so he was left with $[(x/2) - 2]/2 - 2 = (x-12)/4$ diamonds.
When he encountered the third guard, he gave him half of his remaining diamonds and two more, so he was left with $[(x-12)/2] - 2 = (x-28)/8$ diamonds.
Since he was left with one diamond in the end, we can set up an equation:
$(x-28)/8 = 1$
Solving for $x$ gives us:
$x = 36$
Therefore, the thief stole $36$ diamonds.
Another Way (Short Trick):-
To solve this problem, we can start with one diamond left in the end and add $2$ to get $3$. Double it to get $6$ and add $2$ to get $8$. Double it again to get $16$ and add $2$ to get $18$. Double it again to get $36$. Therefore, the thief stole $36$ diamonds.