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?

  • 2
    $\begingroup$ 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.

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    $\begingroup$ 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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