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I came in my office this morning, and there was a piece of paper on my computer screen where I could read:

Make me a hexagon!

On my desk, there were four plastic letters: t, a, n and h. All lowercase.

I don't know who in the world is challenging me early in the morning, but of course I'm gonna make you a hexagon!

Flipping the paper on my screen, I could read:

Your goal is to arrange the letters to make a hexagon. This hexagon will not have curved sides. The letters can't be flipped over or stacked, but rotating them is allowed.

... Well, then let me get my coffee first. What about you go ahead and solve it first? I'll catch up!

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    $\begingroup$ Can you clarify the phrase "This hexagon will only have straight lines"? What does it mean to "have straight lines"? $\endgroup$ – Matsmath Nov 14 '16 at 11:47
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    $\begingroup$ has to be regular? $\endgroup$ – lois6b Nov 14 '16 at 12:01
  • $\begingroup$ @Matsmath Is "no curved sides" better? $\endgroup$ – IAmInPLS Nov 14 '16 at 12:10
  • $\begingroup$ Is the hexagon made up of only letters? And only lower case? $\endgroup$ – Techidiot Nov 14 '16 at 12:13
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    $\begingroup$ @Techidiot But yes, I specified lower case. $\endgroup$ – IAmInPLS Nov 14 '16 at 12:16
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How about

turning the "n" upside down and spelling "utah"? The US state of Utah is a (nonconvex, ~spherical) hexagon.

This is a slightly unsatisfying answer (though I suspect it's the intended one) because

the borders of the state of Utah are curved; lying on the surface of an approximate sphere, how could they not be?

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  • $\begingroup$ I like your answer. However, I feel like there is too much of lateral jump interpreting your answer as a hexagon. Well... so, I am not explaining my concerns very well. My point is that you do not provide a hexagon, as wished by the OP, but rather you provide something which in turn can be interpreted as a hexagon. $\endgroup$ – Matsmath Nov 14 '16 at 13:18
  • $\begingroup$ @Matsmath That's why this is tagged lateral-thinking... $\endgroup$ – IAmInPLS Nov 14 '16 at 13:22
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    $\begingroup$ @Gareth Well, in three dimensions, yes, but in two dimensions, they don't seem to be curved (or very slightly). $\endgroup$ – IAmInPLS Nov 14 '16 at 13:22
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    $\begingroup$ They're close to straight on a Mercator projection, or any other that makes lines of latitude and longitude straight. But not quite! There's a kink in the eastern border, for historical reasons of some sort. $\endgroup$ – Gareth McCaughan Nov 14 '16 at 14:26
  • $\begingroup$ maybe this is why you answer others but not my question about "regular hexagon" @IAmInPLS xD $\endgroup$ – lois6b Nov 14 '16 at 15:29
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The solution:

enter image description here

Because:

Hex, "a" gone

Instead of building an Hexagon (geometric figure) I use the word "Hexagon" and pronunciation "hex" + "a" + "gone" with a little bit of creativity
I form the word "hex" with the existing "h", the "e" is an "a" rotated 180 deg and the "x" is the "t" rotated -45 deg

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    $\begingroup$ I don't get this... Can you kindly over-explain your solution to non-native dummies like myself? Also, in OP there are two parts emphasized in bold face font. Are those parts covered by your solution? If so, then how? $\endgroup$ – Matsmath Nov 14 '16 at 12:53
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    $\begingroup$ But the "a" is there. The "n" is gone. $\endgroup$ – FrodCube Nov 14 '16 at 12:54
  • $\begingroup$ @FrodCube yeah, but the "a" is now an "e" .. ^^' $\endgroup$ – lois6b Nov 14 '16 at 12:56
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    $\begingroup$ @lois6b Even if you count the "a" as gone, the "n" is gone even more and not mentioned in your solution. Apart from this you convinced me :) $\endgroup$ – oleslaw Nov 14 '16 at 13:13
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    $\begingroup$ Nice try, but no cookie for you :-) $\endgroup$ – IAmInPLS Nov 14 '16 at 13:23
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Solution:

A hut

Why?

Take outline of regular huts in a corner view and it gives you a hexagon.

e.g. here and here

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Throw the plastic letters in the trash.

Take the note and use scissors to cut the words "a hexagon" out. Throw the rest of the paper in the trash.

Now all of the letters present have been arranged to make "a hexagon".

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