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The ideas and concocted tools I used to solve these two puzzles allowed me to make this puzzle. Credit to TSLF for the inspiration!

Light up some of the edges in the grid on the left such that the ten digit patterns on the right can be seen without rotation or flipping. The patterns include off edges – in particular no digit can use any of the grid's three missing edges.

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  • $\begingroup$ Since we can't rotate or flip the digits, I don't think there's any (even theoretically possible) way to use the three missing edges as off-segments :-) $\endgroup$
    – Bass
    Sep 25 at 8:59
  • $\begingroup$ @Bass Yeah, my SAT-solving tools tell me that there is still only one solution if the three missing segments are off segments instead. Without restrictions there are 262 solutions in the 2×8 grid (so I tried removing squares until I found a unique solution, which is this puzzle). $\endgroup$ Sep 25 at 9:09
  • $\begingroup$ The other way to check that is to note that for all the three possible digit placements that would include missing lines, there are no digits with all the relevant segments off. $\endgroup$
    – Bass
    Sep 25 at 9:24
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I think I got it.

enter image description here

I started by counting the possible middle segments of the digits, there are 11. This means only one possible location for a digit isn't used.

Taking this into account, the one is as good as placed: that digit's shape is extremely unfriendly to neighbours on the left and the bottom. From there, the 7, 8 and 6 are just about forced, but one must resist the temptation of stacking the 4 on top of the 7. (It takes quite a bit of effort to convince yourself that there simply is no way to fit the rest of the digits in after you do that.)

But as long as you avoid the trap with the 4, the rest seems to work out fine.

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    $\begingroup$ Ah yes, the well-known eleventh digit, backwards F :) $\endgroup$ Sep 25 at 22:16

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