Algebra of apples

Algebra Level 2

A man take some apples from a garden.when he coming out from the garden he passes through three guards.if every guards first take half of the apples (he have) and one extra apple.if passing after third guard he have only one apple,then how many apples he took from the garden?


The answer is 22.

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1 solution

Pramod Harithsa
Oct 10, 2014

Assuming x number of Apple's remain with him before he reaches the last guard

The last take away of Apple can be expressed as,

x - (x/2 +1) =1

Which would give x=4,

Using the same formula for other stages would give X = 22

Guard 2,

x - (x/2 +1) =4 =>x=10

Guard 1,

x - (x/2 +1) =10. =>x=22

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