Help! Can you get my puzzle back?

Question

Puzzling has a lot of really complicated stuff these days, so I just wanted to post a simple Boggle grid.

You know that game, right? You form words by starting from one letter, then taking adjacent letters moving in any of the eight directions, but you can't use the same letter twice to form a single word.

Here are the words you are looking for, they should be familiar to most of you:

time termination tetris nim animals real tangram pattern pangram game anagram flags nonogram

And here is the grid:

Um... that was not what the grid was supposed to look like at all! Have I got one of those newfangled viruses or something?

Since we're already here, can you help me recover my puzzle? I didn't take any backups while I was making this, and I'm really desperate to remember what it was like!

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^{Luckily, the virus or whatever it was seems to have picked colorblind-friendly colors for the image, but if that somehow is still an issue here is a text transcription, in which different letters represent different colors:}

ABCBB
CDEFG
HGABI
JKGGC
LMFMF

Answer 1

The answer:

rtitt
imena
sartp
lgaai
fonon

Explanation:

Here's the initial grid:

ABCBB
CDEFG
HGABI
JKGGC
LMFMF

Start by counting the number of occurrences of each colour (which I'll represent using capital letters):

• A×2, B×4, C×3, D×1, E×1, F×3, G×4, H×1, I×1, J×1, K×1, L×1, M×2

and the minimum number of times we know each letter occurs in the final grid (I'll use lowercase letters for the letters in the eventual grid):

• a×3 (anagram), i×2 (termination), n×2 (termination), o×2 (nonogram), t×2 (pattern), other letters could appear once

There are a total of thirteen letters in the tags (aefgilmnoptrs), and thirteen colours on the grid, so there must be a 1-to-1 correspondence.

I started off by looking at t, o, and n. t must clearly be B or G, as no other colour allows for the adjacent ts in pattern. Looking at all the places we could possibly spell nono (from nonogram), they must either be in B and C (some way round), or else two of F/G/M.

The next letter to check was a. The requirement to spell anagram means we can't have a=C (which would force n into B with a as C, or into D which isn't a valid location for it). We also can't have a=F, as that quickly leads to a contradiction:

ABgBB    ABgBB
gDmao    gDman
HoABr or HnABr
JKoog    JKnng
Lnana    Loaoa

In other words, we've found our first letter position, a=G (immediately forcing t=B to spell pattern).

AtCtt
CDEFa
HaAtI
JKaaC
LMFMF

no now must be MF (one way round or the other). This means that p=I:

AtCtt
CDEFa
HaAtp
JKaaC
LMFMF

If M=n, then we can't spell pangram. Thus, F=n and M=o:

AtCtt
CDEna
HaAtp
JKaaC
Lonon

To be able to spell nonogram, anagram, and pangram, we need K=g:

AtCtt
CDEna
HaAtp
JgaaC
Lonon

To spell termination, we need C=i:

Atitt
iDEna
HaAtp
Jgaai
Lonon

and ADE need to spell erm in some order (for termination); to be able to fit tetris in too we need A=r, E=e, H=s:

rtitt
imena
sartp
Jgaai
Lonon

animals requires J=l, flags requires L=f:

rtitt
imena
sartp
lgaai
fonon

We can find all the words in this grid, so we know it's correct.