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Jul 21, 2019 at 16:46 comment added Penelope Benenati Thank you Max Alekseyev.
Jul 21, 2019 at 13:19 comment added Max Alekseyev If $S$ forms a grid, then a set of points whose labels reveal the labels of the whole set is called a teaching set. There is a bunch of research on minimal teaching sets.
Jul 20, 2019 at 23:56 comment added Penelope Benenati OK, so the problem is not interesting. Thank you.
Jul 20, 2019 at 17:27 comment added fedja If $d=2$, the answer is already $n$ (consider $n$ points on the circle out of which only one (unknown to you) is on the "other side").
Jul 20, 2019 at 14:38 history edited Penelope Benenati CC BY-SA 4.0
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Jul 20, 2019 at 14:10 history edited Penelope Benenati CC BY-SA 4.0
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Jul 20, 2019 at 14:05 history edited Penelope Benenati CC BY-SA 4.0
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Jul 20, 2019 at 13:55 history edited Penelope Benenati CC BY-SA 4.0
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Jul 20, 2019 at 13:47 history edited Penelope Benenati CC BY-SA 4.0
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Jul 20, 2019 at 13:42 history edited Penelope Benenati CC BY-SA 4.0
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Jul 20, 2019 at 13:35 history asked Penelope Benenati CC BY-SA 4.0