# Yes, I mean to say that there is more

Long after the insane Mr. $\Delta\Sigma\Upsilon$ incident, you are resting in the same luxurious mansion. It is, however, most unfortunate (or fortunate, depending on your perspective) that you received a phone call that day.

You pick up the phone. “Hello?” you say into the phone.

“You. Are you the renowned solver who ended that greek guy's reign of terror?”

Greek guy...? Oh, yeah! Him. Gah, I hated that guy. “Yup! That's me.”

“We need you, ASAP. We can't say who we are or why, but it is important. You can meet us at <obscure place, probably an alley> in twenty minutes. *Click*.”

You sit down, rather shocked. All the glory of your past endeavour faded quickly, and you were able to settle down in to a quiet, peaceful routine.

**** routines. I'm doing this!

At <obscure place>

You walk into a clean, modern room. There sits a secretary at a desk to your right. She beckons you come near.

“Welcome. I recognize your face. Mr. $\Lambda\Omega\Lambda$ is waiting for inside.” She gestures to a door, and resumes typing. Oh sheesh. More Greek. What is this, a frat school?! You reach and open the door.

Instantly, a cheery $\tiny{drunk}$ man in a lab coat rushes up to you. “You are a chemistry student! Hooray! And you have a friend! Double hooray! And what's even betterrr is—hey, watch it! ow ow ow!—” The man is dragged away by another man in a light blue lab coat, who seats the oddity. Then, blue-coat walks to you.

“Sorry about that. We had the happy narrator dude out. He was not supposed to debrief you. *Ahem*. I am Mr. $\Lambda\Omega\Lambda$—call me Bob. I have little time to spare. You are to infiltrate a laboratory. I'm not sure where; this is where you come in. If you can solve this puzzle, you're hired. We'll pay you handsomely. By the way, once you get there, you need a passcode. We don't know what it is...”

After some consideration, you say, “I'm up for this. Where is the puzzle?” Bob gestures to a computer. You eagerly take a seat.

(The story is just for flavour.)

# Puzzle 1

You have many tools to solve this problem

Note: there is a typo. “beskeas” should be “bespeaks” I'll fix it when I have time.

Hint 1

"lborders" => "left borders" => ...

Hint 2

The password is not a word in any language, hint 2b and it is the length of half the longest word in this hint.

At the designated place:

You approach the single, solitary man. He looks to you and whispers tersely “Password?”

“I-y-a-O,” you say confidently. Solver: LeppyR64.

He nods. “Come.” You follow him into an obscure door behind him.

# Puzzle 2

“Well, you can only be the Dr. Morigan we have been expecting.” He nods to the table. “We have the sample here. And, in exchange, you will tell us how, no?” You feel a flash of panic. You must act quickly.

“Yes, of course. Remind me--what is the problem? 'Fraid I'm a teensy bit drunk, and my memory isn't the best.”

The man growls something about stupid, old men. “We have a 10-by-10 board. On it will be played the finale of the Fairy-Chess-Piece Championship. We have ascertained from a friend a particularly nasty square-infectious virus. Our scientists have modified this virus to be able to grow quicker, but at the cost of having spread in a different way. That is, it spreads if and only if it has two diagonally adjacent members. We wish to find what is the smallest possible amount of samples sufficient to cover the entire board?

“Oh…I see. Well, I'll try my best—” He glares at you. “—*ahem* I mean, I will not failyou.”

“You'd better not…!” With that, you are locked in the room. I am getting just a little bit tired of being locked in rooms…

As an example, suppose this is where you place the infection:

The next day, the board would look like this:

(If the virus grew at 1 step/day, the intermediate step would look like this:)

• Is 'lborders' a typo too? – Penguino Aug 10 '15 at 2:35
• @LeppyR64 You're smart. No, I was talking about the picture :P The picture contains one purposeful "typo"; all others are unintentional. Sorry for the confusion. – Conor O'Brien Aug 11 '15 at 17:31
• Hmm. The second puzzle definitely has an upper bound at 20, but I'm not confident that it's optimal. – user1618143 Aug 18 '15 at 21:10
• At least two neighbors, or exactly two neighbors? – f'' Aug 18 '15 at 21:39
• Hath you doth forgotten us, oh mighty Conor O'Brien? – Nefer007 Dec 10 '15 at 1:19

## 3 Answers

Twenty virus samples are necessary. A chessboard can be divided into two diagonal meshes with no diagonal adjacencies between them, and the virus can't spread from one to the other just like a bishop can only reach half the squares, so we can consider only the "black" squares and use the same pattern for the white. Furthermore, if we rotate the board 45 degrees, the black squares form a square grid that's easier to work with:

    O
OOO
OOOOO
OOOOOOO
OOOOOOOOO
OOOOOOOOO
OOOOOOO
OOOOO
OOO
O


The virus spreads across this board orthogonally, like the original virus, so the same edge-counting strategy works. It has 38 edges, so we need to start with at least 38/4=9.5 squares infected, rounding up to give us a lower bound of 10. And 10 is indeed sufficient:

    X
XOO
XOOOO
XOOOOOO
XOOOOOOOO
OOOOOOOOX
OOOOOOX
OOOOX
OOX
X


Using the same pattern to infect the white squares gives us an optimal (and easy to remember) solution: completely cover two opposite edges.

Edit: If the virus requires exactly two infected neighbors to spread, and no more, 20 is still sufficient, and the same lower bound applies because it's strictly less contagious. Use this pattern instead:

    X
OXO
OOOOO
OOOXOOO
OOOOOOOOO
XOXOXOXOX
OOOOOOO
OOXOO
OOO
X

• I was just typing it when you posted. By the way, you can also do vertex counting on the main board. – Rohcana Aug 18 '15 at 22:14
• @Anachor: Yeah, but reducing it to a problem that has already been solved was easier. – user1618143 Aug 19 '15 at 2:41
• Good job! That's exactly correct. I will post the final puzzle (puzzle 3) when I have access to my flash drive. – Conor O'Brien Aug 19 '15 at 20:11
• @CᴏɴᴏʀO'Bʀɪᴇɴ Have you lost your flash drive? Now we'll never know how it ends! :-( – wizzwizz4 Dec 13 '16 at 21:13
• @wizzwizz4 I can look for it. I honestly forgot about this puzzle. – Conor O'Brien Dec 13 '16 at 21:15

Since this is a semi-interactive puzzle, here is where to go for the first step...

Go to the corner at M and 5th street.

Using the alt text of the image http://manytools.org/hacker-tools/steganography-encode-text-into-image to decode the image yields these instructions.

The password is IyaO. These are the leftmost letters (or borders) of each line.

If I understand user1618143's answer correctly, then I think this is pretty much the same, but in a more visually pleasing form showing how the virus spreads:

• Yes, that's what you get if you take my solution and mirror the white squares along a diagonal. And then animate it all pretty. – user1618143 Aug 18 '15 at 23:10