Mimosweeper

How to play

You are maturing an antibody-like receptor. A T-cell clone's binding loop (its CDR3) has mutated somewhere, and the mutated version binds the target far better. You have to work out which sequence it is by testing one mutation at a time.

The catch: some mutations make the receptor bind your own tissue instead. Test one of those and the clone is destroyed. You get three.

1 What you are looking at

The grid is a mutation map. Every square is one possible single mutation:

Columns are positions along the loop — position 1, 2, 3 …
Rows are the 20 amino acids, grouped by chemical family (oily ones at the top, charged ones at the bottom).
A square means “the starting sequence, but with this amino acid at this position”.

The starting sequence — the germline — is printed across the top, one letter per column. The square circled below is “position 5, but leucine instead of S”.

germline

Each column is a position; each row is an amino acid.

2 What you are hunting

One hidden sequence — the matured clone. It is the germline sequence with a handful of positions changed. The briefing bar tells you exactly how many positions changed (say 4). Every other position is still the germline letter.

So you are not guessing 20 letters from scratch. You are working out which few positions moved, and what they moved to.

3 Probing — left-click a square

Clicking tests that mutation. You get back one number: how many chemical properties separate the amino acid you clicked from the real answer at that position.

0exact match — that is the residue. The column locks green and is done. 1 or 2chemically close. You are in the right neighbourhood. 5 or 6chemically alien. The answer is nothing like what you clicked.

You get 3 probes per column. After that the column locks and you must work it out by reasoning (a small shared reserve can buy extra probes if you are stuck). Probes are the scarce resource — the whole game is extracting the most from each one.

4 Where the number comes from

Every amino acid has a checklist of nine chemical properties, each either true or false:

Φ oily (hydrophobic) · Ring has a ring in its side chain · + positively charged
C=O has a carbonyl oxygen · N has an amide or guanidinium nitrogen
Sm small · Lg large · OH/S has an -OH or a sulfur · β branches at its first carbon

To compare two residues, go down the checklist and count the entries where they disagree. That count is the number on the tile. Nothing else — no ranking, no fudged “warmer / colder”.

	Φ	Ring	+	C=O	N	Sm	Lg	OH/S	β
A	●	·	·	·	·	●	·	·	·
L	●	·	·	·	·	·	●	·	·
differ						✕	✕			→ reads 2

Alanine and leucine are both oily, but alanine is small and leucine is large. Two disagreements.

	Φ	Ring	+	C=O	N	Sm	Lg	OH/S	β
F	●	●	·	·	·	·	●	·	·
L	●	·	·	·	·	·	●	·	·
differ		✕								→ reads 1

Phenylalanine and leucine match on everything except the ring. One disagreement.

Because it is a plain count, two things follow that you can rely on:

0 means identical. No two amino acids have the same checklist, so a zero can only ever be the right answer — never a near miss.
Readings never contradict each other. Every number you collect in a column is guaranteed to be consistent with the rest, so there is always exactly one answer they all agree on.

Readings run from 0 to 6 in practice. Nine is the arithmetic maximum, but real residues only ever tick one to three boxes and some are mutually exclusive (nothing is both small and large), so the widest real gap is 6.

5 One probe already tells you a lot

Since each reading picks out a whole group at once, a single click splits the alphabet immediately. Probe alanine and the answer is pinned to one of these six groups:

it reads	the answer is one of
0	A
1	G C
2	V L S P D
3	I M F T N E
4	W Q K
5	Y R H

Twenty candidates down to at most six, from one click. A second probe intersects its group with the first, and you are usually down to one.

You do not have to hold any of this in your head — the full checklist for all 20 residues, and a grid of every pairwise distance, are in the Biochemical property panel below the board. Find the row for the residue you probed, and every cell showing your number is a candidate.

6 Worked example — how two probes pin a position

Say position 5 is germline S, and you want to know what it matured into.

you click	it reads	which leaves
A	2	The answer differs from alanine on exactly 2 properties. Only five residues do that: V L S P D — the 2 row above.
F	1	The answer differs from phenylalanine on exactly 1 property. Of those five: V is 3, S is 5, P is 3, D is 5 — only L is 1.

Position 5 matured S → L, found in two clicks and no guessing. That is the core loop: each number rules out most of the alphabet, and two or three of them intersect down to one answer.

Every number comes from the property panel at the bottom of the page — F and L differ only in that F has a ring, so they are 1 apart. You can check any of this by hand.

7 Working the intersections — and the Assist toggle

By default you do this part yourself, using the distance matrix below the board. Probed A and got a 2? Find row A, and every column reading 2 is still in play. Probe a second residue and the answer is whatever survives in both rows.

If you would rather not, Assist in the top bar turns on a possible row under the board that lists each column's surviving candidates and shrinks them for you — when it reaches one letter, that position is solved without even clicking the tile. It stays on until you turn it off again, including across new clones.

Assist is off to begin with because doing the intersections yourself is most of the puzzle. Turning it on makes the game substantially easier.

8 Staying alive

Some mutations make the receptor bind self, and testing one costs a life. They are not random: the briefing bar names the chemical family responsible on this board (say “aromatic”). Only residues in that family are ever dangerous — everything else is always safe to click.

That family is mildly risky everywhere and much more dangerous at a few hidden buried positions, which you have to locate.

The small orange digit in a square's corner counts how many of its 8 neighbours are self-reactive. That is your minesweeper number — use it to tell a safe aromatic from a lethal one.

☠

The three unlit squares in the Y row are unknown. The 1s and 2s around them say how many neighbours are lethal — enough to work out which.

Clicking a safe square also clears its harmless neighbours automatically. That tells you they will not kill you — but it does not reveal their number. Reading affinity always costs a probe.

9 The clues in the margins

Down the left edge, next to each chemical family, is a count: how many residues of that family the finished matured sequence contains. If it says acidic 0, no position matures into D or E — strike both rows off the whole board. If it says aromatic 1, exactly one position ends up aromatic.

Combined with the germline sequence and the number of mutations, these let positions constrain each other. This is what closes out the columns you ran out of probes on.

10 Marking and winning

Left-clickprobe a square (costs one probe). Right-clickcycle a mark: ⚑ “I think this one is self-reactive” → ★ “this is my answer for this position” → clear. Marking is free. Submit clonecommit your answer. Positions with a ★ use that residue; positions without one are assumed unchanged from germline.

Submitting the right sequence wins. A wrong one costs a life and tells you how many positions are wrong, but not which — still useful information.

You can also just probe your way to 0 in every column, but that is slower and riskier than deducing.

11 Scoring — what the K_d means

Your score is reported as a K_d, the real measure of how tightly two molecules bind. It is the concentration needed to occupy half the receptors — so if it takes less to get there, the binding is tighter. The rule to hold on to:

Lower K_d is better. 50 nM is a thousand times stronger than 50 µM.

You start at the best possible score and can only lose ground from there. Two things spend it:

Each probecosts about 3.5% of what is left. Twenty probes halves your score. Each clone lostcosts 60%. Dying hurts far more than being slow.

It bottoms out at the germline value of 50 µM — meaning you found the clone but gained nothing doing it.

probes	clones lost	affinity gain	final K_d
0	0	1000×	50 nM
20	0	490×	102 nM
25	0	410×	122 nM
25	1	164×	305 nM
40	0	240×	208 nM
40	2	38×	1.3 µM

A well-played 12-position board takes roughly 25 probes, so the middle of that table is a good game. The 0-probe row is unreachable — you cannot solve a board without probing it — it is just where the scale starts.

Watch out for one thing: because lower is better, the K_d in the top bar counts upward as you do worse, which is backwards from most scores. It is labelled K_d if won because it is a projection — what you would bank if you submitted a correct clone right now, not a measurement of the board. The win screen also shows the fold-improvement, which moves the intuitive way.

12 Difficulty — Naive, Primed, Memory

The selector in the top bar picks the board size. Changing it starts a new clone immediately.

The three names are the actual life history of a lymphocyte, and they are ordered by how much mutation has accumulated: a naive cell has never met its antigen and is still close to germline; a primed cell has met it and is responding; a memory cell is the end product, carrying the most changes. So the harder the tier, the more mutated the clone you are chasing.

	Naive	Primed	Memory
positions to solve	10	12	15
mutations to find	3	4	5
hidden contact positions	1	2	3
self-reactive squares	~12	~15	~20
probes per position	3	3	3
spare probes (reserve)	8	8	6
lives	3	3	3

Four things get harder, and they compound:

More positions — simply more columns to resolve before you can submit.
More mutations — every position you cannot solve is a coin flip rather than a safe “assume germline”. The more of them there are, the less that fallback is worth.
More contact positions — the dangerous chemical family is far more likely to be lethal at those buried spots, so more of them means more self-reactive squares and more chance the residue you actually need is sitting inside the danger zone.
A smaller reserve — and this is the real squeeze. Memory gives you 6 spare probes across 15 positions where Naive gives 8 across 10. Proportionally it is less than half the slack.

For scale, playing well and wasting nothing, a solved board takes roughly:

	typical probes to solve	total budget available
Naive	~22	38
Primed	~25	44
Memory	~33	51

There is real headroom in all three — but that assumes probes chosen well. Wasted probes come out of the same pot, and every one of them also costs you score.

Assist is not part of the difficulty. It is off in every tier and toggled separately whenever you like — so a Naive board with Assist on is much easier than a Naive board without it.

13 If you only remember three things

Click anything to start. Low number = close, 0 = correct.
Read your number off the distance matrix below the board: the probed residue's row, every column showing that number, intersected across probes.
Only the one chemical family named in the briefing can ever hurt you.

The property table and distance matrix are below the board under “Biochemical property panel”. Reproducible boards: ?seed=12, and &reveal=1 shows you the answers.