One thief entered a cave where he found a pile of diamonds. At first he thought of taking all. But listening to his conscience he thought of taking only half of them. But while returning he picked up two more from the pile. After that Second thief entered the cave and bagged half of remaining diamonds and picked up two more while returning. Later third thief entered and did the same. Even the fourth thief did the same. When the fifth thief entered he found only one diamond in the cave. How many diamonds are there in the cave at first.

• Total diamonds in the cave at first = x
  First thief took x/2 +2 So remaining is x/2 - 2 i.e (x-4)/2
  Second thief took (x-4)/4 + 2 he left (x-4)/4 -2 i.e (x-12)/4
  Third thief took (x-12)/8 + 2 he left (x-12)/8 -2 i.e (x-28)/8
  Fourth thief took (x-28)/16 + 2 he left (x-28)/16 -2 i.e (x-60)/16
  Now the remaining diamonds after fourth thief left is given as 1
  So (x-60)/16 = 1
  that means x = 76
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