25
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The Setup

Consider a 5-by-5 grid of 7-segment displays, "smashed together" so that the peripheral segments of neighbouring displays overlap (see below).

           a smashed 5-by-5 grid of 7-segment displays

You are given a particular grid as follows:

                                                     a smashed 7-segment grid with black segments

The grid contains the 20 characters:

                                   list of characters appearing in the 7-segment grid

All of the characters appear in the grid, and some appear more than once. They are arranged in such a way that no two "on" (coloured) segments overlap.

For example, an A cannot appear immediately to the right of a b, but may appear immediately right of C. A 3 may not appear immediately above a q, but may appear immediately above a y.

The Challenge

Given

  • the coloured segments must match the given pattern
  • all 20 characters must be used at least once
  • no two coloured segments may overlap

can you determine which characters are displayed on all 25 7-segment displays?

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  • $\begingroup$ Lovely idea for a puzzle! As shown by evidence, it lends itself to solving by program which is not exactly cheating but still less fun. So I wonder, in constructing this puzzle: Do you think this can be solved (to a large extend) by logical deduction or will it be trial and error mainly? $\endgroup$ – BmyGuest Jul 24 '15 at 11:53
  • $\begingroup$ @BmyGuest: It's definitely not as sequential and procedural as, say, sudoku, but deduction plays a part in the sense that the puzzle can be solved incrementally (to a degree), and fixing errors in the "error" part of the procedure is a very structured process of propagating excess segments from one part of the puzzle to other parts where segments are needed. This is essentially the same as the familiar "here are 30 tetrominoes; can you fit them perfectly into this rectangle?" puzzle, which is a well-known combination of deduction and trial-and-error (i.e. depth-first search). $\endgroup$ – COTO Jul 24 '15 at 19:29
  • $\begingroup$ Am I the only one who wonders if this could be exploited to 'hide' a message? ;c) $\endgroup$ – BmyGuest Jul 24 '15 at 20:32
  • $\begingroup$ @BmyGuest: It's a neat thought, and you certainly could. The main problem is that there are far easier ways to hide a message in plain sight. ;) $\endgroup$ – COTO Jul 25 '15 at 2:26
20
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There are three valid patterns:

EPrFA hq337 A7-L8 CP2ny b9-ed (-, 3, 7, A and P appear twice)
P2rFA Pnq37 ECELA Lhy-8 b9-ed (-, A, E, L and P appear twice)
P2rFA Pnq37 FCELA Chy-8 b9-ed (-, A, C, F and P appear twice)

Or, as graphics:

EPrFA hq337 A7-L8 CP2ny b9-ed P2rFA Pnq37 ECELA Lhy-8 b9-ed P2rFA Pnq37 FCELA Chy-8 b9-ed

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  • $\begingroup$ Your solution #3 was the one I constructed. Good job. ;) $\endgroup$ – COTO Jul 13 '15 at 12:23
  • 2
    $\begingroup$ Thanks. I wrote a small program to tackle this and happened to find two more. (Nos 2 and 3 differ only in the stacked EL and FC halfway down the left columns.) An interesting puzzle. $\endgroup$ – M Oehm Jul 13 '15 at 12:37

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