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This question already has an answer here:

Anyone who plans to visit the Miracle Fruit Tree in the Royal Garden has to travel through Seven Gates in each of the Seven Curtain Walls surrounding the garden.

Each of these gates has a guard.

There is only one way in and out each of these curtain walls.

The Royal rule is Each of the guard will take half the number of fruits from anyone on the way out.

One fine day, a commoner negotiates a deal with each of the guard on the way in.

The deal is after sharing the split, will take back one from the guard.

After plucking 'MAGICNUMBER' number of fruits on the way out, Both the guard and the person honor the deal at each of the Seven gates.

At home the Person counts all the Miracle Fruits remaining.

The count is 'MAGICNUMBER'.

What is the 'MAGICNUMBER' ?

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marked as duplicate by Ry-, Mark N, JLee, Community Jun 12 '15 at 17:20

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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The person would only need 2 magical fruits
Half of 2 is 1, and he gets 1 back which is 2 again.
This will work for an infinite number of gates.

Alternatively,

The person could have 0 magical fruits.
Half of zero is 0, so there is no loss
Then the guard give you 1 fruit!
You end up with 1 free magical fruit to eat!

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  • $\begingroup$ You got it. (Hope this was not a duplicate question) $\endgroup$ – kanchirk Jun 12 '15 at 16:38
  • $\begingroup$ @kanchirk I think it is :( $\endgroup$ – Mark N Jun 12 '15 at 16:38
  • $\begingroup$ Let me delete it then. Sorry. $\endgroup$ – kanchirk Jun 12 '15 at 16:39
  • $\begingroup$ @kanchirk I will vote close it once I find the dup. $\endgroup$ – Mark N Jun 12 '15 at 16:40
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    $\begingroup$ Thank you very much. Appreciate it. This was a puzzle for my kid. $\endgroup$ – kanchirk Jun 12 '15 at 16:41
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Here's how I solved this:-

MAGICNUMBER/2 + 1 = MAGICNUMBER

MAGICNUMBER/2 - MAGICNUMBER = -1

-MAGICNUMBER/2 = -1

MAGICNUMBER/2 = 1

MAGICNUMBER = 2

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