I have an opaque 6-sided die. Without using mirrors or any other optical aids, what is the greatest number of faces of the die that I am able to see at the same time?
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$\begingroup$ You only need to see three sides to know where all six sides are, so you can comfortably look from afar at it. I can then see the other three sides in my imagination. $\endgroup$– pokeJan 15, 2015 at 9:12
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3 Answers
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Due to the fact that the die is smaller than the distance between the eyes, if you hold it die very close to your face, it's possible to see 5 faces at the same time (all faces except the one opposite to you):
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6$\begingroup$ Technically, using some medical tools to bash one's face in, one might even be able to see all six sides :D $\endgroup$– dmgDec 3, 2014 at 12:59
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12$\begingroup$ @dmg I'd consider it part of puzzle standard conditions that medical "enhancements" of involved creatures is not allowed. Otherwise I might as well just bash the teeth out of a certain fox in order to cross a river without it eating my chicken. $\endgroup$ Dec 3, 2014 at 13:17
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4$\begingroup$ Did you try if it is possible to see all six faces if you hold a corner towards your face? It depends on the angle between your eyes and the opposite corner of the die. With a small die and a favourably shaped skull, it might be possible even without enhancements. $\endgroup$– JiKDec 3, 2014 at 14:38
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4$\begingroup$ @JiK I tried, it isn't very far from being possible, but it is definitely not possible with my head. $\endgroup$ Dec 3, 2014 at 16:07
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3$\begingroup$ @rumtscho It doesn't need to be all that close, there is no theoretical limit to how far away the die can be while the eyes are still on the correct side of the faces. But you'll get a better angle by holding the die closer. I get the best view around 15 cm, I can focus, and I can tell all the pips apart. $\endgroup$ Dec 3, 2014 at 21:25
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You didn't specify the material the die can be made of. Dice made of translucent plastic are common, and you can easily see all six sides.
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2$\begingroup$ Nice try, but I think I covered that with the word "normal". $\endgroup$ Dec 3, 2014 at 15:12
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9$\begingroup$ I'm not sure that your usage of the word 'normal' implies that the die is opaque - usually it is taken to mean a die that is in the usual shape of a cube (if it has 6 sides). $\endgroup$ Dec 3, 2014 at 15:28
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10$\begingroup$ I think commercially available in thousands of stores nationwide & online qualifies as 'normal'. google.com/search?q=red+translucent+dice&tbm=shop $\endgroup$ Dec 3, 2014 at 15:30
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1$\begingroup$ In any case, it is a question about me and my die, my die is opaque. $\endgroup$ Dec 3, 2014 at 16:09
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If your goal is to be able to see the most number of sides of a normal opaque die without any sort of aid, whatsoever, besides your own hands and eyes, then i'd say w0lf's answer is the best.
However if your goal is to see the most amount of sides of a normal opaque die without the aid of optical tricks but by utilising other tricks, then i'd suggest simply cutting off the faces of all six sides, thinly, line them up and you will be able to see them all, with an added bonus - the insides of the die! :O
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4$\begingroup$ @Richard, it would be a normal die, then you cut it up into 6 tinier normal dice. But the original die was normal. :D $\endgroup$ Dec 3, 2014 at 20:01
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