# Some of the clues seem to be missing

The answer to this puzzle is a four letter word describing its theme. The clues appear incomplete yet there is only one answer.

# Key:

3x?: 0000?00 3x3: 0?10110 3x7: 00??111

2x6: 11001?0 ?x?: 01?0101 3x6: 00000?0

2x4: 11001?0 2x3: 10?1010 1x7: 00?1111

1x5: 001?110 1x8: 00101?0 1x2: ?000000

2x8: ?011010 1x?: 00?0000 ?x5: 100110?

2x2: 11?0110 1x3: 001011? 3x4: 0?00000

3x8: 1?11?10 2x1: 11?0110 2x5: 1001?00

3x1: ?0000?0 1x1: ?0000?0 ?x4: 00000?0

# Cipher:

A..Z0..9

U+2TNNL 8+EF7OR D+8EF0 V+FWPCR 7+1GKTX 2+ED0B 8+IYEIQ U+2TRQI 8+D03E B+KNKHD V+FWNFQ

Hint 1 (updated 04/04/23):

Hint 2:

In the key fragments, the part left of the colon is independent of the part on the right. For example, for the key fragment labelled 2x4, the label does not help to find the missing bit in 11001?0.

Hint 3:

The key fragments are given in groups of 7 bits, some of which are missing. What data protocol is sent in 7 bit pieces, which is resistant to transmission noise?

Hint 4 (related to Hint 1):

There are too many bits to fit in the grid shown in Hint 1. There are $$24\cdot7=168$$ bits given and only $$32\cdot3=96$$ slots available. What are the extra $$72$$ bits for? How can it be decided which bits to keep and which to discard?

Hint 5 (spoilers for the key):

Yes, there really is parts of the key missing. There's nothing in the description/title/key definition that will help you get the rest of it.

• Time to add a new hint? Mar 25, 2023 at 20:06
• @Techidiot I would, but not sure how to without giving it away. Thanks for the reminder though, I'll give it some more thought Mar 26, 2023 at 21:29
• looks like rot13((7,4) unzzvat pbqr jvgu 3 cnevgl ovgf, naq 4 * 24 = 96) Apr 4, 2023 at 8:42
• @LukasRotter yep, that's correct for part 1 Apr 4, 2023 at 11:47

Posting an answer because I don't think there's much interest left in this one. I would appreciate tips on how to make better puzzles in future.

# Key

## Positions

The first step is to figure out how the key fits together. The clues are given in the form axb: {string of bits}. First, we rearrange the clues in order of a and b, as follows:

Some of the clues' positions are still unknown, but they can be deduced. The unknown positions are:

1. 3x?
2. ?x?
3. 1x?
4. ?x5
5. ?x4.

There is only one entry missing in the 4th and 5th columns, so the last two positions must be 1x4 and 3x5. With these filled, there is only one possibility left for the first and third clues - 3x2 and 1x6. Finally, the second clue can be filled as 2x7. This reveals the full grid:

## Bit strings

This part is a little more tenuous, but I'd hoped that the format of seven bits with missing/unknown parts would lead the solver to think of error correction. A well known error correction scheme with this format is the Hamming(7,4) code, which is the format I used for this puzzle. The Hamming code requires even parity in the following groups of bits:

1. 1st, 3rd, 5th, 7th
2. 2nd, 3rd, 6th, 7th
3. 4th, 5th, 6th, 7th

Following these parity rules, the full bit strings are revealed:

Taking just the data bits of the Hamming code (3rd, 5th, 6th and 7th), putting them in a 32x3 grid, and filling just the ones gives the following:

There is a mistake on the 7th character (it should be aligned left), but the key spells out --O-T-ON (ie. Bad luck! There's still pieces of the key missing).

# Cipher

The cipher used is a simple Vigenere substitution. The first line shows the alphabet used for the cipher (ie. abcdefghijklmnopqrstuvwxyz0123456789). The key is incomplete, but using the provided alphabet to perform a partial decoding of the encrypted text gives the following:

?+?F?4? U+1??A? U+?02? ?+1?6?D U+??6?E ?+00?? U+?F?4D ?+?F?7? U+0??0 ?+1?64? ?+1?4?C

I chose the missing letters carefully such that the keen-eyed puzzler should notice a 'U+' or '?+' at the start of each space-delimited group. By enforcing the start of each group to be a 'U', the remainder of the key is revealed to be 'ABORTION'.

Fully decoding the cipher gives the following plaintext:

U+1F64D U+1F6AA U+0020 U+1F64D U+1F6CE U+000A U+1F64D U+1FA7A U+0020 U+1F64D U+1F47C

These are Unicode references. Translating these to characters gives the following:

🙍🚪 🙍🛎

🙍🩺 🙍👼

This is a reference to the infamous webcomic Loss, which is the theme, and final answer to the puzzle.

• I guess error correcting codes aren't very familiar to the Puzzling community. Also, using alphanumeric (rather than just alphabet) is probably unfamiliar for Vigenere. Sep 26, 2023 at 15:00
• Ok, thanks for the feedback. Is that the only issue? Say you were familiar with error codes - do you think the puzzle would have been fun to solve? I tried to mix it up from a standard cipher question by using the encrypted text to figure out the key. Sep 26, 2023 at 23:09
• Seems quite fun! Kinda unlucky it wasn’t solved. The theme actually fits quite well with the loss of bits and the loss of the baby. I also noticed that you gave hint 1 a day after posting. Without that hint it would be rather difficult so perhaps consider putting it together with the puzzle. Good luck on your future ciphers. Sep 27, 2023 at 11:12