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You are on your way to your friend's house. You decide to carry 2 apples to your friend. To get to their house, you must pass across 8 gates. At each gate, the keeper will take half the amount of apples you have and return one apple back. The question is, how many apples should you carry at the beginning?


marked as duplicate by Alconja, boboquack, Quintec, JMP, El-Guest Sep 11 '18 at 1:58

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    $\begingroup$ if there was a lateral thinking tag: start with zero apples, walk through the gate, throw your apple over the next gate, then you will have two apples! $\endgroup$ – Yout Ried Sep 10 '18 at 19:48
  • $\begingroup$ And that's why I didn't include it, cuz I know some people have an infinitely broad imagination! $\endgroup$ – Wais Kamal Sep 10 '18 at 19:53

You need

2 apples.

This is because

Each gatekeeper will take one apple (half of two) and return one to you, meaning you keep the same number of apples through each gate.

  • 1
    $\begingroup$ Haha.. Just missed it! :) $\endgroup$ – Vivek Parekh Sep 10 '18 at 15:49

I am not sure if it's this easy. But here's a try.

You need to carry only 2 Apples. At each gate, the keeper will take half the amount i.e. 1 apple and will return it. At the end, you are still left with 2 apples.

  • $\begingroup$ Close one! I think I barely beat you in, but great answer nonetheless! :D $\endgroup$ – El-Guest Sep 10 '18 at 15:49
  • $\begingroup$ That's correct, but @El-Guest answered first :) $\endgroup$ – Wais Kamal Sep 10 '18 at 15:49
  • $\begingroup$ @El-Guest I guess yours is. $\endgroup$ – Vivek Parekh Sep 10 '18 at 15:49
  • $\begingroup$ Yeah, very close :) $\endgroup$ – Wais Kamal Sep 10 '18 at 15:51


Let’s work backwards: (2 apples - 1) * 2 = 2. Therefore, you only need to bring 2 apples.


You could only bring one apple, and walk through the gates and back. Then you should have around 1.8 apples. Then leave the .8 and repeat for infinite apples! :P

  • $\begingroup$ Ah, I see now. I will change my answer $\endgroup$ – Rohit Jose Sep 10 '18 at 15:46
  • $\begingroup$ Nice one (never thought of this tbh)! $\endgroup$ – Wais Kamal Sep 10 '18 at 15:53
  • $\begingroup$ @Wais Kamal And neither did the gatekeepers, apparently! $\endgroup$ – Rohit Jose Sep 10 '18 at 15:54

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