# You're invited! Now what?

### (semi-interactive puzzle)

BRIIING! BRIIING! BRIIING!

You wake up with a start. It's 6:30... already!? Darn. You roll slowly out of bed, preparing for the day ahead.

Whatever preparing you did then was really inadequate to prepare you for what came next. Not even close!

After taking a shower and eating a surely-nutritious breakfast, you make your way to the door. As you extend your hand to the doorknob to open said door, you see a shadowy blur heading to the door. Recognizing that the object wouldn't stop kindly and ring the doorbell before entering your house (so rude!), you dive backwards; the door explodes into lots of pieces, and the object comes to rest a foot or two away from your feet.

Who on this good earth would do that...?! You rush to the door to see if you could find the perpetrator; nothing! You proceed to pick up and examine the object, placing it on the nearest table.

It is a large package! As much is obvious. No outer markings. You make to open the package; doing so reveals another package, and another until you have 10 such package wrappings. (A package in a package in a package...) At the end of this package chain, there is a small envelope.

# Puzzle 1

***holes! Who the heck would use this much packaging to wrap a package?!!??! You think to yourself. An image of a vexed Al Gore flashes in your head before you open the envelope. It reads thus:

Dear [name]:
So sorry to wake you up so early. At least, we apologize for you having to get up so early. Apologies are very important!! We LOVE LOVE LOVE LOVE the length of our apologies--they are also very important! You're important to us. Unless you fail... heh.
You have been invited. In order to show your worth, we will not tell you where, but, rather, we will give you a puzzle.--

--To find this puzzle--your invitation--you must first and foremost solve the puzzle on the back of this sheet.

You eagerly flip the sheet around. On it, is written thus:

A fisher is hungry for a large sum of fish, so he decides to fish for some fish. In his local pond, there are three types of fish: small fish, which weigh 5 units; medium fish, which weigh 25 units; and large fish, which weigh 125 units. The farmer catches 35 fish. Of the fish that the fisher caught, $m$ were small fish, $2m$ were medium fish, and $q$ were large fish. The combined amount of small fish and medium fish is $5m$ less than the $\blacksquare$ root of the amount of the large fish. How many large fish ($q$) did the fisher catch?

You sit down, perplexed. This isn't a riddle! This is poppycock! There is not enough information, and--! You stare at the paper. That's when it hit you...almost. Something's there, you're not entirely sure what, however.

Indeed, you ask yourself: “What is the value of $\mathbf{q}$??

Hint 1

When the puzzle tells you something is important, you should listen to it. The puzzle is inclusive of the entire letter.

Hint 2

The entire second line is the apology.

Apology & Hint 3
It seems that a crucial part has been tampered with, by the displaying of the, erm, apology in the second line.

Do now look at it again; perhaps you will understand...

More story; to be read after solving Puzzle 1; (Answer in below story text; is therefore spoiler-marked.)

“$q=256$!” you shout out loud. “That took long enough! I don't even know what an apology is, anymore...”

You hear a high-pitched whistle and instinctively cover your ears. Gah! What is that!? The whistle then ends, and outside, a man peers through your door intently. “Hello, there,” he says to you.

“What the 'ell do you want?!” you practically shout.

“It is not what I want that concerns me. As it seems, you have solved the puzzle.”

“Some puzzle! Who would think to look in the apology for the net amount caught?!” At this point, you are letting out your vexation on the (poor) man.

“We did make it plain that it was crucial to the puzzle's solution. That is beside the point, however. Now, I extend to you the opportunity to acquire an invitation.”

“But the letter said—”

“I did not see the letter—only the apology. Ergo, I do not heed else instruction. So, do you wish to acquire the invitation, or shall I put this pitiful abode to my back and forget about you?” The man looks at you expectantly, as if you really had no choice.

You sigh. “Alright, then. I'll go for it. What do I have to do?”

# Puzzle 2

“Here ya go,” the man says matter-of-factly to you, handing to you another sheaf of paper. On it is written thus:

The best of the best! Your home contains the answer. For in it, you'll find five children, children of a great number; well-rounded children. You'll take the best of the children (make sure you have five!) and add them up.

After reading the text, you look up to the man. He says, “Tell me the number when you're done. Do you have a seat I could use?”

“Erm... yes. Please, come in. Take a seat—any seat,” you say as you take your own seat, staring at the next in the series of cryptic puzzles. What is the final value...?

Hint 1

'Your home' refers to the home in which we all dwell... you, me, and al'thor... everyone you know here.

(moar story) Your visitor turns to you. “Times 'a tickin'!” he says to you, smiling vexatiously.

“This is timed!?” You shout. You hadn't known that there was a timer going!

“Why, yes! You must solve it soon—I'm rather tired... if you get my drift.” The visitor stands, bows mockingly, and continues to sit. As if an annoying ##### like him deserves to sit down even on a porcupine! you think to yourself, but soon, your mind drifts elsewhere. The solution... I don't get it—

420!” you shout once again. You turn to your visitor, who stares at you, mouth agape. (Solver: @rand al'thor. Solution)

The visitor fumbles with his words. “B-But you weren't supposed to...” He inhales deeply and regains composure. “Very well. It seems as if you will be receiving the invitation. So, here it is:” At this point, you receive another letter.

Dear [name],
It was in the unlikely event that you should receive this letter; then again, if you completed the last puzzle, you must be surrounded with people who might be good at this type of thing. This does tell me, however, that you are indeed worthy of attending.
This letter is an invitation, of which you must bring to the event. It will occur on [date not-so-long-away] at [obscure location in a wealthy neighbourhood]. I do expect your presence there,
truly yours,
Mr. $\Delta\Sigma\Upsilon$.

“Huh!” You exclaim. “What a chance!”. Mr. $\Delta\Sigma\Upsilon$ is one of the wealthiest citizens in your country and is famous (or infamous, according to others) for his puzzle-books. He is a recluse, and hardly a soul has seen him, much less gotten to know him, save his closest associates. A thought briefly flashes through your mind before it slowly sinks into your subconscious. This thought was that ever since its foundation, the Puzzling SE has been loathed by Mr. $\Delta\Sigma\Upsilon$. Your visitor extends his hand to you, and you take and shake it. It is settled! You're going.

(Later, on aforementioned date at aforementioned location) You are dressed in your best formal attire. You have a nice pair of shoes. You brushed your teeth. You combed your hair. You are one fashionable-lookin' person as you walk into the luxurious hall of the grand house. In it, you see a few others milling about, observing the hall. You also look around, trying to find a familiar face or two.

In the hall, you find no such face; only strangers of whom you have never seen. At once, a man steps into the hall and shouts, “The doors are now closed!” Upon him saying this, all the doors (and windows and any other chance of escape) closes, and the hall is effectively sealed. Some of the people in the hall attempt to pry open certain windows and doors, but to no avail. The rest of your remain in close attention to the new guest to the room.

“What is it that you want from us?” one of the guests growls. More shouts of complaint arise from the crowd. “Who the hell are you?” shouts another voice. The man raises his hands, and all fall silent in a few moments.

“I am Mr. $\Delta\Sigma\Upsilon$. You are here tonight because of your prowess and superiority to others in the realms of puzzle-solving. Now, I give you a final dichotomy, of which you must either accept or refuse very soon. That is this: you will either work for me, or you won't. Choose quickly.”

At once, a few of the voices speak up in “Yes”s confirmation. These people walk forward to Mr. $\Delta\Sigma\Upsilon$, who signals them behind him. You, however, are smarter than that and know of the terrible living conditions of which those who go to work for him.

The person who first complained says no defiantly. Mr. $\Delta\Sigma\Upsilon$ glares at him. “You have sealed your fate.” Mr. $\Delta\Sigma\Upsilon$ then brandishes a pistol and fires two shots. There is one less person in the hall.

Instantly, a mass of people surges behind Mr. $\Delta\Sigma\Upsilon$ in allegiance. Only you and a few others remain. The remaining people, in a moment of indecision, fail to answer.

“Then, I guess you few cannot decide. I will give you one day. Until then... sleep tight!” He and his new workers withdraw through the last remaining door which closes behind them, and all is dark and quiet.

Moments later, a dim bulb flickers amongst the visitors remaining. As it turns out, said a person had brought a flashlight (in case of an emergency), perfect for such an emergency as this. He introduces himself as Robert.

What seems like an eternity later, the door opens, and a sliver of light is let in, and in steps Mr. $\Delta\Sigma\Upsilon$. “Listen up. You must make your choice now. But, you being puzzlers (and persistent ones, at that!) are now offered a choice of freedom. You must solve the puzzle I give to you. But here's the catch: If you cannot solve it in one days time, you will be forced to work for me. Don't pretend that you can escape through law and justice—money trumps both. Good luck.” Mr. $\Delta\Sigma\Upsilon$ again leaves the room, and what remains is your puzzle.

(TL;DR) You've been captured. Solve the puzzle or else suffer a horrendous fate.

# Puzzle 3

There is among the pile the following items:

1. A letter.
2. A gun, with bullets sufficient for each one of the people remaining, of which there are 6. Each bullet is numbered, $1$ through $6$.
3. A box, with a bullet-shaped hole. Is a little larger than the size of a bullet, and seems like it could carry one.

On the letter is written:

Oh, let me tell you the tale!
'Tis a tale of woe.
Surely, you must fail!
Now, go go go g.o!
Now that I know you, am like yo.u,
you never seem to help.
With you, it's like one step forward.s
and two steps bac.k.
I climbed the stairs
until I stood at the top
and counted the stairs I too.k
and threw them at yo.u.
You fell down to the ground,
I smiled with glee.
Then, to my surprise,
you pulled me down below yo.u!
Then I remember the times,
when we danced around the squar.e,
I dropped two penny down the wel.l.
You dropped half of the pennies lef.t.
Now there's half of me left on the floo.r,
The other was poured out for you.
Now, take a bullet! Take one only.
Shoot me!

(This is the last part. Good luck!)

Hint 1a: Out of frustration, you turn the letter over. On it is written:

Sulp 48! IT!!!!!!! I'm so backwards, haha!

“What on earth....?”

Hint 1b:

Backwards... Backwards... Oh...! Reversing the text of the back, you get: !!!!!!!TI !84 pluS, the name of a commonly-known calculator. Then, perhaps, the solution will have to do with numbers...

Hint 1c:

In the end, you will need put a bullet inside the box-thingy. Since these bullets are numbered, you must figure out exactly which bullet to put in the box.

Hint 2:

Certain lines in the poem are instructions.

# Epilogue

You hear a loud KNOCK on the door. But this time, you are prepared. The door swings open at a tediously slow rate; your heart races.

You have the second bullet in the bullet-shaped chamber, as per request of one of the puzzlers stuck in the room (Solver: Nefer007)

Suddenly, the person who told you to choose the second bullet loads said bullet in the gun. What are you doing?! You think. He aims the gun at the door, and...

“Ah hah! I see you haven't solve the puzzle! I guess that means you must—” You will never know what exactly Mr. $\Delta\Sigma\Upsilon$ was going to say, for at that moment the puzzler squeezes the trigger and KA-BOOM! the bullet enters and exits the fiend, and with a solid thump, he lays still on the ground.

A moments silence ensues. Soon, the entire mansion erupts with happy cheering. With rapt glee, puzzlers and workers alike flow from the doors of the mansion. After a while, only a few puzzlers remain.

These puzzlers introduce themselves to you. The first introduces themselves as Chadi Abou Sleiman, and shakes your hand. “I should get back home, I was working on a project for Android, you know how it is.” Smiling, the person departs.

The second introduces himself only as rand al'thor. “This was fun! I'm sort of sad that it's over, now...” After a pause, “Well, maybe not. See you around, maybe!” He then departs.

The last puzzler introduces himself as (first) the man who shot the fiend, and (second) as Nefer. “He was going to kill us anyways. Or enslave us. Besides, he was a bastard, and all bastards gotta die.” He winks, and leaves, walking through the doors with confidence.

And then, it is just you in the empty hall. You hear a sink running in the mansion. Then, it dawns on you: Who is to own this house...! You gather the bullets into your pocket, claim the second bullet from the late owner of the mansion, and head towards the nearest housing agency.

LATER

You sit at your new home: the beautiful mansion. You're loaded. You split all the cash you found in your house equally amongst the puzzlers who were there, and you're still loaded. You found out that, if you had chosen the wrong bullet, it would have done nothing, is made of a flimsy pseudo-metal that would have been incinerated in the chamber of the gun.

You sigh. What to do... You take out your laptop, and log on to a familiar puzzling site. You click on a puzzle. What fun!

This is a test run of the semi-interactive puzzle type. Make sure to read about semi-interactive puzzles in the link at the top of the question.

• You shouldn't be equating the m+2m+q with 35 - the farmer and fisher are (I'm assuming) two different people. Commented Jun 16, 2015 at 20:38
• When you say amount do you mean number or weight?
– Bob
Commented Jun 16, 2015 at 20:56
• There are red herrings in this pond ... Commented Jun 17, 2015 at 21:14
• It's sooo frustrating. Lol, egads man, I don't even know what an apology is anymore. Commented Jun 20, 2015 at 17:56
• Tell me exactly how you can throw stairs. Sounds like a nice party stunt. Commented Jun 25, 2015 at 0:50

## Puzzle 1

There are m small fishes, 2m medium fishes and q large fishes. Therefore the first (1) equation should be: $$m+2m=\sqrt{q}-5m$$ $$8m=\sqrt{q}$$

The second (2) one: $$m+2m+q=T$$ $$q=T-3m$$ Where T is the Total number of fishes that the fisherman caught. (T is different than 35 assuming the fisherman and the farmer are different)

Replacing (2) in (1), squaring and rearranging gives the following quadratic equation: $$64m^2+3m-T=0$$

This equation gives an integer value for m for a high increasing number of T

If T = 67, m = 1 and q = 64

If T = 262, m = 2 and q = 256

If T = 585, m = 3 and q = 576

If T = 1036, m = 4 and q = 1024

....

If my logic is correct, there should be a relation between one of those values and the hint about the importance of apologies which I'm not able to figure out.

Edit

The "apology": So sorry to wake you up so early. At least, we apologize for you having to get up so early. Apologies are very important!! We LOVE LOVE LOVE LOVE the length of our apologies--they are also very important! You're important to us. Unless you fail... heh. contains:

256 characters. Therefore, q = 256

• Very well done! You're almost there! I suggest you reread the front of the letter and ponder the importance of Strings. Commented Jun 19, 2015 at 17:41
• The apologies are 256 characters, so i think the answer is q=256. Commented Jun 20, 2015 at 16:18
• Yeah.. You're right! Now that the OP has edited the question and added some extra space, the "apology" has grown from 252 to 256 characters! I'll wait for a confirmation by the OP if q = 256.
– CAS
Commented Jun 20, 2015 at 16:33
• @ChadiAbouSleiman Wait no longer. Congrats! You got it. Commented Jun 20, 2015 at 16:37
• Thanks ! After hint 2 I knew it was something related to the characters length of the sentence but after obtaining 252 I dropped that idea. Thanks also for @TroyAndAbed for poking me about it. I'll edit the answer now
– CAS
Commented Jun 20, 2015 at 16:59

## Puzzle 2

I'll have a crack at this as well, following TroyAndAbed's idea.

The best of the best! Your home contains the answer. For in it, you'll find five children, children of great number; well-rounded children. You'll take the best of the children (make sure you have five!) and add them up.

I interpret this as follows.

"Your home" is Puzzling.SE. The "five children" are the five highest-voted questions. As of today these are as follows: "Well-rounded" means we round the numbers of votes say to the nearest 10 (this is a good idea since those numbers are going to change over time). Then the top 5 questions have scores of 110, 80, 80, 75 (let's say round this up), and 70. The total is 420, the final answer (coincidentally the answer to Life, the Universe, and Everything with an extra 0 on the end).

• Congratulations! You got puzzle #2! I love how the $420$ worked out, don't you? Commented Jun 23, 2015 at 20:09
• @CᴏɴᴏʀO'Bʀɪᴇɴ Wow! I wasn't really expecting this to be right. Just goes to show... Commented Jun 23, 2015 at 20:13
• Not sure if I like this puzzle though. It's going to go out of date within a few weeks or months (as I also commented on Troy's answer). Commented Jun 23, 2015 at 20:14
• Ahh shoot. I forgot about that. Is there any way to get the wayback machine to take a snapshot ? Commented Jun 23, 2015 at 20:22
• @CᴏɴᴏʀO'Bʀɪᴇɴ Sorted! Commented Jun 23, 2015 at 20:38

## Puzzle 1

Assume that the message isn't saying "Square root" but rather "[REDACTED] root". The equation we're balancing goes from:

m+2m+q=35 and m+2m=5m-sqrt(q)

to:

m+2m+q=35 and m+2m=5m-q^(1/k)

If we are allowed to choose k ourselves, and if k is non-integer, we can balance the equation for q=32,29,26,23,20,17,14,11,8,5 and 2. However, balancing the equation for those values of q produces an integer k in exactly one case: at q = 32, we get:

m+2m=5m-q^(1/k)

1+2=5-32^(1/5)

1+2=5-2

Therefore the fisherman caught 32 large fish.

• Wow. Nice answer! Unfortunately, $\blacksquare$ root does indeed render as "Square root". Commented Jun 16, 2015 at 20:39
• Also, it is "5m less than the square root", not "5m less the square root". Commented Jun 16, 2015 at 20:59

Puzzle 2:

Following your hint, the home is:

Puzzling Stackexchange

And the best five childrens (of the week) are rand al'thor, Joe Z, Aggie Kidd, A.D, CodeNewbie

Taking the best of each children:

rand al'thor: 3 gold

Joe Z : 4 gold

Aggie Kidd: 2 gold

CodeNewbie: 1 silver

Adding all this, the finale value is:

16

• close... very close... younger children... Commented Jun 23, 2015 at 1:36
• Edited with users of the week Commented Jun 23, 2015 at 2:41
• This is going to be subject to a lot of change over time though ... Commented Jun 23, 2015 at 10:13

## On segment 3:

There are four instances of go. This probably isn't important at all, but it's starting to feel like everything is important here...
Noticing the misplaced periods, we get...

ouskkuueltr

which is a eleven-letter string with 1 o, 3 u, 1 s, 2 k, 1 e, 1 l, 1 t, 1 r and backwards reads

rtleuukksuo

The verses contain the operations: +1-2, rounded up rounded down to 0 (I think,) then something about an increase (likely?,) multiplication, the current result squared, minus 2, minus half of the remainder. Possibly rounded down and then maybe -1. The answer is a number between one and six, as per the remaining bullets.

The clue about the TI 84 Plus (a graphing calculator) gives us the numbers 48 and 84.

Obvious steps to answer: Figure out what we are multiplying by and figure out what number we start with.

A few minutes later, after some bowls are placed to remind us where each bullet is...

Four instances of the word go... 4... +1 -2 is 2... times its square is 8... -2 is 6... halved is 3... minus 1 is 2...

You set bullet 2 aside just in case. Actually, you load the gun with that bullet, just so if he walks into the room and you haven't solved it yet, you can give him a loud surprise.

• I'm also coordinating the steps to solve this and save us all. Commented Jul 3, 2015 at 15:50
• Getting close... Commented Jul 5, 2015 at 1:13
• idea I think I have a starting point. Commented Jul 5, 2015 at 16:27
• cheers You got it! Great job, you solved puzzle number three. Commented Jul 5, 2015 at 19:51
• Isn't 4 + 1 - 2 = 3? Commented Dec 15, 2016 at 6:08

## Puzzle 3

Given Hint 1b, I suspect the solution involves

the positions of the keys on a TI-84 Plus calculator, which can be seen in the following image:

Let's look again at the poem.

Now, go go go g.o!

This might suggest we should start from the ENTER key.

With you, it's like one step forward.s
and two steps bac.k.

One step up and two steps down (more or less) take us to the (-) key.

I climbed the stairs
until I stood at the top

Go all the way up to the VARS key or maybe even the TRACE key.

and counted the stairs I too.k
and threw them at yo.u.

Six to eight, according to what we count as the top.

you pulled me down below yo.u!

This is probably something to do with a fraction.

when we danced around the squar.e,

The $x^2$ key?

I dropped two penny down the wel.l.
You dropped half of the pennies lef.t.

Half is the reciprocal of two, so maybe we should be looking at the $x^{-1}$ key, which is adjacent to the $x^2$ key.

I'm still not sure about the last two lines, nor about the interpretation of the misplaced full stops in the poem.

• Nice work! Regrettably, the TI-84 hint was only meant to get the puzzler to think about numbers. Commented Jul 3, 2015 at 23:35
• @CᴏɴᴏʀO'Bʀɪᴇɴ That was a waste of time then. Oh well. Is Nefer007 any closer? Commented Jul 3, 2015 at 23:37
• Yes, he is on the right trial by interpreting the verses as mathematical operations. Commented Jul 5, 2015 at 1:12
• Maybe not correct, but certainly a nice effort Commented Jan 27, 2016 at 23:00

Solution

# Puzzle 2

Solver: @rand al'thor
Solution

# Puzzle 3

Solver: @Nefer007
Solution

• I suggest you incorporate this into the question instead. If this information is only written in an answer that looks like it's going to languish far down the page, it's almost useless! Commented Jun 23, 2015 at 21:20
• Or accept this answer as the 'correct' answer so it appears at the top of the page.
– Bob
Commented Jun 24, 2015 at 0:06
• @Bob that's also a good idea. Commented Jun 24, 2015 at 0:16
• @Bob An accepted answer doesn't float to the top if it's posted by the OP. Also, questions with accepted answers get less attention because people assume they're already done and dusted. Commented Jun 24, 2015 at 14:25
• @randal'thor I did not know that (about floating to the top) useful to know if a bit annoying given that here on PSE the OP is likely to have the 'official' answer.
– Bob
Commented Jun 24, 2015 at 17:05

Puzzle 2:

My guess is

The Stackexchange Network

And the five best well rounded children are

The top stackexchange sites!
Stack Overflow (9.6m questions)
Mathematics (454k)
Super User (270k)
Server Fault (198K)

The best thing about the children are the

Questions!

10.715 million!

## Puzzle 1

Based on a reply by the Puzzle poster to Chadi Abou Sleiman I have to conclude that the value of $q$ is related to the 'size' of the string. I.E. The space taken in memory to store the apology. However it's not a subject I am adept enough with to find the right numbers and patterns.

I believe it has something to do with base 64 math or 64 bit encodings because: $q = 64m^2$ which means $q$ is any square multiple of $64$.

Start with: $$m + 2m + q = X$$ And
$$m + 2m = sqrt(q) - 5m$$ $$8m = sqrt(q)$$ $$64m^2 = q$$

Beyond this I haven't figured out the exact values yet.

The Apology is 91 characters, 20 words.

• See the poster's response to my request for clarification about Hint 2 in the comments for the question. Commented Jun 20, 2015 at 1:14

I'm thinking the total number the fisher caught is 175, since 6:30 is highlighted in the puzzle. My reasoning is that 6:30 is the ratio between the total fish caught by the farmer and the total caught by the fisher or 1:5. So if the farmer caught 35 fish, that would mean the fisher caught 175. I can't work out q using this though so I might be wrong or just bad at math or both.

• I thought that too at first, however I think it's just to display an alarm clock style format, kind of like the black square is just decor. Plus it's not listed under the "puzzle" heading Commented Jun 19, 2015 at 21:07

I'll post my line of thinking as an answer so whoever feels like, can follow my lead.

The trick there is that either we assumed farmer and fisher were the same person, or that farmer's fishes were irrelevant.

The key I feel goes in the lines of the combined amount taking into account both the fisher and the farmer fishes.

Being $m, 2m, q$ the small, medium, large fishes of the fisher, and $x,y,z$ the same for the farmer we have the following:

\begin{align} x+y+z&=35\\ (x+m)+(y+2m)&=\sqrt{z+q}-5m\\ x+y+8m&=\sqrt{z+q}\\ (x+y+8m)^2&=z+q\\ q&=x^2+y^2+64m^2+2xy+16xm+16ym+48xym \end{align}

The key would be that $m,q,x,y,z$ must be integers. Even though, this has many solutions, so some other restriction has to exist within the letter.

# Puzzle 1

I started with $$m + 2m = \sqrt q - 5 m$$ to try to find a couple integers that fit the problem, and I found $64 - 40 = 24$, leading me to this:

$$q = 4096, m = 8, 2m = 16$$ but the sum of those is much larger than 35.

Then, when rereading, I found that the puzzle said that the "farmer" caught 35 fish, and it doesn't say anything about the fisher.

So one possibility is that the fisherman caught 4096 large fish?

I haven't found what I am supposed to do with the weight of the fish though...

• Actually, with only the sqrt(q) - 5m = 3m requirement, it seems like any perfect square multiple of 64 would work. q = 64, m = 1, 2m = 2? Commented Jun 18, 2015 at 16:42

# Puzzle 1

If the farmer catches $x$ small/medium and $y$ large fish, then we are given $$x+y=35$$ $$m+2m+x=\sqrt{q+y}-5m,$$ so $$q=(8m+x)^2+x-35=64m^2+(16m+1)x+x^2-35.$$ If $m=0$, we need $x\ge6$ to make $q$ nonnegative, so $q\ge 7$ (with equaliy if $x=6$). If $m>0$ then certainly $q\ge 64-35=29$. These solutions seem weird as the farmer seems to be better at fisching than the fisher, but sometimes such puzzles implicitly ask for tha smallest possible solution. So that would be

The number of big fish the fisher caught os $7$

Or let's just say

The number of big fish the fisher caught is of course $q$

Or alternatively

If they serve so much fish, I don't care to be invited.

# Puzzle 1

Is Q

1024

If we do the equation for the fish I ended up getting

m = 4

by inferring from the length of apologies (8, 12) and the overuse of the word LOVE(although I don't know if that's really relevant) if that's the case and we apply it to the length of the apologies, 8 and 12 it means that

m = 4
2m = 8
5m = 20
12 = sqrt[x] - 20 = (12 + 20) ^2 = 1024
q is then equal to 1024 or 32^2

I'm not a mathematics guy so I hope no one freaks out on my lack of ability here, but I thought I'd give it a go.

The answer to puzzle 2 is:

562
Your Home is converted to ascii values.
The top 5 are mooru.
Mind I haven't necessarily taken care of the well-rounded comment but that might be because I don't use Stackoverflow in a standard font? I definitely left out the Y because of that.

• Nice try! But sadly, incorrect. Commented Jun 21, 2015 at 1:39

Where did I go wrong?

If m = small fish, 2m = medium fish, then 3m = small & medium fish. Therefore,(equation 1) 3m + q = 35.

3m is 5m < q, so:

(eqn. 2) 3m = sqrt(q) - 5m, therefore: (eqn. 3) 8m = sqrt(q)

Substitution eqn. 3 into eqn. 1 gives us:

(eqn. 4) 3m + 64m^2 = 35

Therefore, m = 0.7164 - a non-integer, and therefore eqn. 4 is not true.

• Where did you go wrong? The farmer is different from the fisher. So the fisher didn't catch 35 fish. Commented Jun 17, 2015 at 20:37
• Honestly, I don't even think this is a valid answer. Commented Jul 5, 2015 at 20:55