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Disclaimer: This riddle MAY have been given elsewhere. I heard this one a few months ago from a friend, and I have no idea what his source was.

You're in a room, since that's your job. Your singular apparatus, is of course, a bucket of sand. It is very important to you, and indeed, vital to your job. You know exactly how many grains of sand are in your bucket, and are very proud of this fact.

However, one day, tragedy strikes and a absent-minded secretary spills her mug of spaghetti sauce into your bucket! After much mourning, you pour out the tomato-basil flavoured mess in your bucket, and replace the sand. Distressingly, you realize that you don't know how many grains of sand are in your bucket anymore!

But, as luck would have it, a man comes and claims he knows exactly how many grains of sand are in the bucket. Indeed, he boastfully claims he can tell you the exact number of grains of sand particles in any vessel at a glance, and happily offers his services.

However, due to legal issues, he claims he cannot tell you the number of sand particles in your bucket before you hire him.

How can you confirm that the man knows exactly how many sand particles are in your bucket or if he is simply a charlatan seeking a quick cash grab at the heels of a tragic event?

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    $\begingroup$ Welcome to Puzzling User12429, I am glad to see you are eager to contribute to this Stack Exchange (although I do not know if this is a duplicate)! I have edited you post with some grammatical improvements. $\endgroup$ – Mark N May 14 '15 at 19:03
  • $\begingroup$ Ah, thank you for that! Wrote the thing out in a bit of a rush, didn't have time to look over it. $\endgroup$ – TheWamts May 14 '15 at 19:11
  • $\begingroup$ Is the main problem here to find out how you can prove what he tells you is right, or to try and get him to give you an answer? (or possibly something else) $\endgroup$ – Mark N May 14 '15 at 19:12
  • $\begingroup$ The main question is to prove that the man's claim is indeed correct, and not just him mouthing off. You are allowed to ask the man anything, unless it would allow you to discern the specific number of grains yourself. (I.e. you can ask him if the bucket contains more than 10 grains, but you cannot ask him how many grains is 1 tenth of the total number) $\endgroup$ – TheWamts May 14 '15 at 19:15
  • $\begingroup$ Listen, I don't know anything about your sand; I've got a jar of dirt $\endgroup$ – Dacio May 15 '15 at 5:37
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Fill the bucket with lot of sand and show it to the wizard.
Change room, remove some grains (count them!), then show again your bucket to the wizard.
Now, ask him: "How many grains were removed?".
If his answer is correct, he's telling the truth about his powers.
Of course, you may think that he's just lucky. If so, repeat the experiment again!

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  • $\begingroup$ Once you did this and confirm he is always right. Couldn't you just empty the bucket (into another bucket) and ask him? (So you don't even need to hire him! If you are frugal) $\endgroup$ – Mark N May 14 '15 at 19:20
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    $\begingroup$ He would answer "All the grains were removed" $\endgroup$ – leoll2 May 14 '15 at 19:21
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    $\begingroup$ Through leoll2 answer, the man's not telling you the number of grains in your bucket (not even indirectly), so he would answer. Even though, through Mark N's answer, he'd indirectly tell the number you wanted to know, so he wouldn't answer. All together: Great answer, leoll2. $\endgroup$ – Masclins May 14 '15 at 19:25
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    $\begingroup$ That doesn't prove that he can tell how many grains of sand is in a given bucket. He could be a mind reader, for example. $\endgroup$ – Fax May 14 '15 at 20:49
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    $\begingroup$ @BaileyM, or you could scoop the removed sand into a jar and put it in your pocket. After the wizard tells you how many grains were removed from the bucket, count the grains in the jar to see if he's right. $\endgroup$ – cjm May 14 '15 at 22:09

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