Lights out, 7-segment version

Question

Given a 7-segment display with some segments switched on and some off, find a sequence of digits (0-9), such that after toggling the corresponding segments for each digit, all segments are switched off.

Example

  _
  _    [3] =>     |   [1] =>    [OFF]
  _               |

Numbers and their corresponding segments:

 _         _   _         _    _    _    _    _ 
| |    |   _|  _|  |_|  |_   |_     |  |_|  |_|
|_|    |  |_   _|    |   _|  |_|    |  |_|   _|

Rules

Codegolf ⊨ shortest entry wins.

Input

A non-empty list of segments which are switched on, given as

1. A sequence of numbers. Segments are numbered from top to bottom, left to right; starting from 0 or 1. Numbers need not be in order.

2. A single 7-bit digit. MSB/LSB not specified (thus you can choose).

Non-numeric characters between numbers are allowed (but not required to be supported).

Eg. for number 7: 136 or 1010010 or 0100101

Output

A sequence of numbers to be "applied" to the display. Not restricted in any way, such as order of the digits. Eg. for initial state corresponding to number 1, valid outputs would be 1, 111, 010, etc.

An alternative output is a 10-bit digit (again, MSB/LSB is your choice). Eg. for 1 as input, the output would be 1000000000 or 0000000001.

Some combinations have several non-repetitive solutions, eg. segments corresponding to the uppercase letter H can be switched off by 013, but also 489 and 0258.

If no solution exists (which I believe is not possible), the output is empty.

Answer 1

Jelly, 26 25 bytes

2ṗ⁵’µ×“wØ][:koR¶{‘^/=µÐfḢ

Try it online!

Takes input as a 7-bit integer. Returns the binary form of a 10-bit integer.

This just brute forces all possibilities. Remove the Ḣ to get all possible outputs or replace it with an X to get a random possible output.

Magic Visualization Program!

How it works

2ṗ⁵’µ×“wØ][:koR¶{‘^/=µÐfḢ  - main link, takes one integer
2ṗ⁵’                       - generate all length-10 binary arrays
    µ                µÐf   - now we find those arrays which correspond to digit-
                              sequences which work to switch off all segments:
                              Filter (keep) those arrays which:
     ×                      - multiplied by 
      “wØ][:koR¶{‘          - [119, 18, 93, 91, 58, 107, 111, 82, 127, 123] 
                               (encoding for turned-on segments given number)
                  ^/        - reduced by XOR
                    =      - are equal to (implicit) the program's input
                        Ḣ  - output the first of these valid arrays

Answer 2

JavaScript (ES6), 117 107 101 86 84 bytes

Saved 15 bytes thanks to Neil

Takes input as a 7-bit integer, where the LSB is the upper segment. Returns a 10-bit integer where the LSB is digit 0.

f=(n,k)=>[83,0,57,73,10,71,87,1,91,75].reduce((n,v,i)=>n^=k>>i&1&&v+36,n)?f(n,-~k):k

Demo

f=(n,k)=>[83,0,57,73,10,71,87,1,91,75].reduce((n,v,i)=>n^=k>>i&1&&v+36,n)?f(n,-~k):k

console.log("'1' shape", "-->", f(0b0100100).toString(2))
console.log("'7' shape", "-->", f(0b0100101).toString(2))
console.log("'H' shape", "-->", f(0b0111110).toString(2))

Answer 3

JavaScript (ES6), 60 bytes

n=>[65,35,55,42,48,54,110].reduce((r,v,i)=>r^=n>>i&1&&v+v,0)

This works because:

• Toggling 1 and 7 toggles the top segment only
• Toggling 1, 2 and 6 toggles the top left segment only
• Toggling 1, 2, 3, 5 and 6 toggles the top right segment only
• Toggling 2, 4 and 6 toggles the centre segment only
• Toggling 5 and 6 toggles the bottom left segment only
• Toggling 2, 3, 5 and 6 toggles the bottom right segment only
• Toggling 2, 3, 4, 6 and 7 toggles the bottom segment only

Answer 4

Mathematica, 40 bytes

BitXor@@{260,802,10,514,3,266,293}[[#]]&

(It may be golfed more by choosing output for each segment carefully and switch between LSB and MSB.)

Take input as a list of positions for example {2,4,5,7} and output a 10-bit number (384 = 0110000000 in binary) in MSB order (0,...,9).

In the example it correspond to

  |_
  |_

and the output correspond to {7,8}.

Explanation:

The magic numbers (hardcoded list) is the output which is returned for each segment. (encoded in binary) And, if a number appear in the list twice, the effect is the same of it not being appear, so bitwise XOR is used. We just need to XOR the output of possible value of the segments turned on.

Answer 5

Jelly, 12 bytes

ị“A#7*06n‘^/

Try it online!

This does not brute force, and it is remarkably shorter than my other solution. Takes input as a list of turned-on segments, and outputs as LSB is top segment.

Output as list of digit moves.

How it works

This is going to be quick

ị“A#7*06n‘^/ - main link, takes input as a list of turned-on segments (eg. [1,3,6])
 “A#7*06n‘   - list literal [65,35,55,42,48,54,110] where each element is a 7-bit
                 integer, where each integer corresponds to how to turn off
                 a segment (eg. turn off the first segment with 7 and 1 =>2^7+2^1=>64)
ị            - get the elements in the list corresponding to the input indices
          ^/ - XOR reduce these elements to get a single 7-bit integer