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Puzzles Reinvented
So, we have A LOT of puzzles to get through this time. Let's get cracking!
3. Thirdly, take A's layout and imagine that B is looking at it from the left.
Working from left to right in B's description, each row of matchboxes would contain a maximum of:
2 piles x 2 layers
3 piles x 1 layer
2 piles x 1 layer
2 piles x 2 layers
So the maximum possible number of matchboxes in this case would be 20.
S. Finally, take the layout that A described from above and imagine that B is looking at it from the top of A's top-down description.
Add up the number of matchboxes as shown in Hints 1-3. If this number is higher than 20, you know it's your answer.
Now all you have to do is count the matchboxes.
It's all a question of perspective. You can take this from any angle on the ground and since that affects the number of boxes in each column...
Not much in the way of dialogue for even pseudo-hidden puzzles. We're quite accustomed to that, though, I feel.
2. Seven days after 70 days ago is nine weeks ago. So if that day was a Sunday, what day would it be today?
3. Seven days before 70 days from now is the same day of the week as seven days after 70 days ago. If today is Sunday, all this puzzle is asking you is what day of the week it will be nine weeks from today. Pretty simple, eh?
S. If you know what day of the week it is, you'll always know what day is X weeks before or X weeks after because it will always be the same day!
Well, 70 is 10x7 so...
3. The note is an equation, consisting of two three-digit numbers.
Take a closer look!
S. "121 - 113 =" is what's written on the paper. If you can find the answer to that, you have the answer to the puzzle.
Believe it or not, we're almost able to finish Picture Book 1 already! I know, I'm shocked too.
But, well, it's right there in the name. Book 1...
3. Continuing from Hint 2, move back to the space before the banana skin you first slid on.
S. Continuing from Hint 3, it should should be obvious which path you need to take. Use the next banana skin you encounter to slide all the way to the wall and walk to the goal from there. If you accidentally slip on a banana skin, it might be better to start again.
3. Half the birds fly away and one comes back. Then half the birds fly away again and one comes back again. Etc. etc. etc.
The number of birds always ends up the same as it started. The answer is so simple, you don't even need to calculate anything.
S. The phrase "half of them fly away" is the tricky part. In this puzzle, "half" means just one bird!
Get it now?
It's an overly complicated way of describing something incredibly simple. Good to see no one got tripped up.
It's a hidden puzzle so it might as well not have post-puzzle dialogue for all the difference it wouldn't make.
3. Out of the nine digits, the ones that are only used once are 2 and 7. The room numbers that contain these digits are 29 and 71. You have to visit these rooms either first or last.
S. If you start from room 29, the order is 29-49-54.
If you start from room 71, the order is 71-18-38.
And if 29 and 71 are the start and end of your rounds...
And now we're into mandatory puzzles, so there's no dialogue we haven't seen before for most of these.
At least we got the last sticker for Book 1 out of this. We could fill it in now and get Book 2, but I'll hold off until we can clear them all.
3. Try finding the kind of rectangles talked about in Hint 2. You can create two horizontal rectangles using the centre square and the square to its left or right.
S. You've got to draw a line through one of the two rectangles talked about in Hint 3.
Think about the angle of this line.
Technically there's four right answers here, but they're reflections/rotations of each other. Kind of a moot point, really.
The solution here doesn't acknowledge it, but a diagonal from the bottom corners is also 100% valid.
3. The bones on the X-ray show up white. And you know those are real, so...
As was pointed out, there is something unusual about this mouse. It really SHOULD just be showing its skeleton...
Unfortunately, that it's not is in itself is a bit of a clue!
S. Hmm...
If things that are really in the patient's body, like bones, appear white, then the dark objects must be somebody's idea of a joke!
But there is one white thing in there that looks suspicious...
It's times like this that I'm reminded about another famous British puzzle solver. Once you eliminate the impossible...
Now Luke, let's not jump to any conclusions. Andrew is quite the prankster himself.
It's entirely possible that he placed this fake X-ray here to shock his visitors.
If that's the case then it certainly worked on me. I was really worried for a moment there!
3. When you align the keys just so, the secret number will appear.
S. Keep the blue key on top, and rotate the yellow key 180 degrees. Touch the teeth of the keys together and...
I wasn't entirely sure if this one would work in thread that well. It's easy enough to see from the blue key alone, I think, which is why I went with it anyway.
That no one seemed to get it wrong sure corroborated that. And even noticed the trick as-is for good measure.
Suspicion
The doctor instructs the pair to head to the back of the hospital, where they find the Laytonmobile.
Luke and Layton head for the Gilded 7 Casino on Flatstone Street.
One added benefit to this game being more story focused is that chapter breaks make sense for once. They're not just arbitrarily strewn about, and half of them aren't just blatant filler either!
More London Streets
Before we head on back to Flatstone Street, let's take one last quick look at the Laytonmobile before we leave her here for a while.
Hmm... Let's focus on what we're sure of for now.
The author of this letter is Luke Triton. In other words, Luke, the sender is you.
We've been following his directives all this time.
Perhaps meeting him face-to-face will shed some light on our current situation.
Let's head to the Gilded 7 Casino.
Yes, let's! I can't wait to get to the casino!
All right, Professor. It's a shame we can't drive there, though.
Unfortunate as that may be, it doesn't look as though my car will be going anywhere soon.
Never mind. After all, the best way to do the legwork for an investigation is on foot.
Ha ha! I couldn't agree with you more, my boy.
Since we probably won't be back any time soon, let's go say goodbye to Dr Schrader. Good chance we won't see him again after all!
A Quiet Town
...oh.
Well, our visit did seem to put him in high spirits. Perhaps he ventured out for a walk.
Ah well, doesn't matter. In fact, it's beneficial that he's not here. He was hiding a Hint Coin under his pillow, the rascal!
Also since it's on the way out, let's ask Natalia what she knows about this casino.
Yeah, there is one, but I'm not sure it's the kind of place you can take kids...
Don't worry, madam. We're just meeting a friend there.
Do you happen to know where on Flatstone Street the casino is located?
Hah, sorry. Not my scene. You should ask someone in the area.
Yes, I suppose a resident of Flatstone Street would be able to tell us. Thank you.
We've no reason to stick around here, so we'll just head right on back to Flatstone Street then. Just gonna skip past the subway...
More London Streets
Yes, but I can't see anything around here that looks like a casino.
I think our best bet would be to ask a local.
Oh look! There's someone we can ask! Wait here, Professor.
Well, the best person to ask would be--
Yes, exactly what I was going to say. Good work, Luke, but... maybe not quite this one.
I-I'm very sorry, sir!
I gather that didn't go very well, Luke?
Let's ask someone else, Professor. I can't even look at that man without him snapping at me.
And all this time I thought you had a talent for communicating with wild animals! Ha ha!
Don't laugh, Professor! That man was scary!
Now now, don't look so sour. I was only trying to lighten the mood a little.
Why don't we find someone else to help us?
How convenient that there's someone new here to ask!
I couldn't agree more.
It's the perfect day to find a nice grassy spot near the river - or to go for a walk.
Speaking of walks, my hubby and I came up with this great puzzle while we were out one day.
Hmm, maybe if I had a guarantee of some useful info. As is, we'll just skip this for now. Sorry!
So, I guess we'll just look around for someone else to ask. Someone more reliable.
Someone like Edgar. Good ol' reliable, trustworthy Edgar.
What? Why are you scared of me?
You? No, it's your friend there with the b-b-big hat! Augh! He's looking right at me!
Please calm down, sir. I mean you no harm. You must have me confused with someone else.
The only thing I want to know is the location of the Gilded 7 Casino. It is around here, isn't it?
The casino?
And if I do, you're going to send me on a one-way trip to nowhere!
What are you talking about?
Augh! Somebody help meee!
Poor fellow. It sounds as though he's had a run-in with someone who looks like me.
He's not the first person to react strangely to your hat.
He's not! We've even been through this before. With Edgar, no less.
Hmm. Yes, it seems my doppelganger has quite a fearsome reputation.
Well... Maybe you should take your hat off for the time being. Just to avoid confusion, you know.
Nonsense, Luke.
...Yeah, that.
Er... I suppose not. Well, what's our next move?
That girl from the hotel, Becky, has been quite helpful. Let's try asking her for directions.
This sounds like a good plan, and the hotel IS right there.
But we'll ask this guy about it first. We'd be passing by him anyway and all.
No, sir. You misunderstand me. We aren't going there to gamble, merely to-
A casino ain't no place to take a child! Even I know that!
Wow! It's really nice of you to worry about me.
Indeed, but you really needn't be concerned about the boy's well-being. Especially when-
Look mate, you don't take kids into a place like that, and that's the end of it.
What a nice thug. Let's just ignore his warning, enter the hotel and ask a young lady about it.
Searching for Clues
Yes. We're supposed to meet someone there.
Well if you say so... But I think you ought to know that the place is a favourite Family haunt.
We appreciate your concern, Becky, but we really do need to go there.
All right... Oh good, Granny's asleep again.
Oh... Er... We don't need to worry about our safety, do we? Not that I'm scared or anything.
Tee hee! Good! Bravery is an admirable character trait, even if it can get you into trouble...
So anyway, you know where Flatstone Street Station is, right?
Just head north from the square in front of the station. You'll see the casino eventually.
Ah, I had a feeling it was somewhere round there.
You did? How come?
I thought there might be something dodgy up there, but I couldn't get past him to see for myself.
Well, you might be all right this time.
Those thugs move around from post to post pretty often.
Good to know.
That sounds like a completely terrible security system!
...I literally just said that, Becky!
Go and see for yourself, there's a good chance you'll be able to pass now. I... Uh-oh!
Yeah, see, I dunno about that. Right now, that's exactly what we want.
No need to worry, madam. Becky was just giving us directions to our next destination.
Oh, is that so? Well, as long as she's being helpful.
Actually, y'know what? Before I forget, let's head back a ways. We're gonna nip into a small building while we're in the area..
Puzzles
Ah, here we are. I don't see Granny Riddleton around here, but the giant flower is still incredibly conspicuous...
Also it's worth noting that this entire scene is voiced, but I'm just gonna skip over that for once.
Now Luke, I'm sure he won't hurt us as long as we don't bother him.
If you say so...
You know, I've never seen a bee quite like this. Can you try talking to him, Luke?
I suppose I can try.
So, I mentioned voice acting and Beasly here is voiced by.... actually, I don't know. At all! They're uncredited.
But in the Japanese release, he's voiced by comedian Tetsuya Yanagihara who... I've heard as Skull in Katekyo Hitman Reborn! and Yeager in Yu-Gi-Oh! Arc-V. And out of his tiny list of roles, that's it. I've heard him in absolutely nothing else. 
Wow, you're not like any bee I've ever met.
Isn't that what I just said? Well, it's true. I'm no run-of-the-hive bee, but I do try to blend in.
You'd probably have better luck blending in if you didn't talk.
Sure, whatever you say, smart guy. But listen, I've got something you should hear.
You see, I have what you might call one of them "magnetic personalities".
Wait, are you saying you've got the same job as Granny Riddleton?
Yeah, uh, so instead of Granny Riddleton, the hypothetical "lost puzzles" character this time around is... a bee.
Also he explains how to get the lost puzzles, but we don't care. I'm just including this pun because it's bad and he should feel bad.
Really just takes the sting out of the whole scene.
More London Streets
Since we've passed by him once already, we'll talk to Max on our way back to Flatstone Street.
A new puzzle, eh? Where'd you find it, Max?
It's a secret. But if you solve the puzzle, I'll tell you. What do you say? Want to try it?
Sure!
I'm gonna step in here and tell Luke he's wrong. We'll do it later. We've got places to be!
So we'll just move on from here past the hotel and back towards the subway station.
That's no ordinary bird, Luke. It's a parrot. How do you suppose it got here?
Let's ask him! Hiya, Mr Parrot! Where did you come from?
Ho ho! I think you may have been a bit too eager there, my boy. You scared him off!
Aw. I was Just trying to be friendly...
To say that conversing with animals is meant to be Luke's special signature trait, he's managed to succeed at it a whopping... zero times on-screen so far.
Honestly, I like that Luke has never pulled it off because it avoids the issue of "okay so Luke is literally Dr Dolittle and that's basically just magic".
It seems Becky's guess was spot on. Let's keep moving north.
And as soon as we go further north from the station...
Flashback
Silence
We suddenly have a scene of Layton and Luke walking through the streets of London. I do appreciate that this makes them look more inhabited than we've seen. You can explain that as a gameplay conceit (and also not wanting the DS to choke and die) easily enough, but it's good they didn't forget it when it matters.
But, the reason this is an animated cutscene is because of this... one lady.
And how the Professor is surprised to see her!
She kinda looks like what I'd imagine an older Flora to look like, honestly. But that can't be it, since she just walks by without a word...
...And that sure wouldn't get this reaction from Layton!
Oh!
He straight up turns and stares as she walks past and out of sight. It's like he's seen a ghost or something.
As Layton just stares in surprise, suddenly a woman starts talking...
In fact, this particular woman here is voiced by Lani Minella. You might recognise her more as the American voice of... Luke Triton. She doesn't sound awful here, so her Luke voice being garbage is clearly just the result of bad direction.
...Hershel, please. You're in a fancy restaurant. Please take off the cap. You don't wear hats indoors like that!
It's rude!
Layton being embarrassed is a very unusual sight to see, but it's nice that we're finally getting to learn something about him.
In the third game of the trilogy named after him.
Also seeing him be bashful like this is surreal. He's normally just nothing but confidence and surety (even when he's off-guard!).
End
More London Streets
Is something the matter, Professor? You look dazed.
I...I'm fine, Luke. I thought I saw... No, my eyes must have been playing tricks on me...
Does it have something to do with that lady who just walked past?
Hence the flashback, yes.
But that brings the scene to an end, and we're finally somewhere new. We'll just talk to this guy who's blocking our path...
We're on our way to meet someone at the Gilded 7 Casino.
I see. Going to the casino to "meet someone", are you? Interesting. Veeery interesting...
Psst, Professor, I think this man is trying to intimidate us.
Stop that whispering, boy! I'm right here, you know!
Oops! Um... Sorry, mister.
Hmph. Well, since you've apologised, I suppose I can overlook your rudeness this time.
I'm sorry to impose, sir, but would you be so kind as to let us pass? It's getting rather late.
But of course, my good man. As soon as you solve this puzzle of mine, that is.
Mandatory puzzle. Just gonna skip past that...
Danger lurks about that hat of yours. You'd best watch yourself around here.
Jeez, Ward. Tell us something we don't already know!
Why is everyone so fixated on my hat? Do you know someone else with a hat like mine?
...You know what, I can't even pretend to get mad at that.
And Ward is the last thing blocking us from reaching the... outside of the... casino!
I think it's safe to say that we've found the Gilded 7.
I can't wait to see what it looks like up close!
There's a hidden puzzle in the fountain here. Being a hidden puzzle, it's dialogue amounts to "there's a hidden puzzle here!" so I'll just include it with the others. Now let's try and go on into the Gilded 7!
Membership card?
The Gilded 7 Casino is a haven where society's finest ladies and gentlemen can gather.
We check membership cards upon entry to ensure that less savoury types are kept out.
Hmm... This is certainly the first I've heard of such a policy.
I don't suppose you'd be willing to make an exception for us?
If you can solve this puzzle, I'll let you in without a card - just this once, mind.
This fellow seems awfully focused on your hat as well.
Naturally. Is there any greater proof of one's gentlemanly nature than a fine top hat?
For once, it is for a positive reason instead of fear and worry. That's nice to see.
Anyway, a puzzle was here. It's down with the others now.
You've certainly earned the right to enjoy our exclusive facilities. Welcome to the Gilded 7.
For what it's worth, the original Japanese name for the casino is the "Lucky Casino 7". Yeah, it flows just a tiny bit weirdly when translated like that.
Silence
I know you're excited, Luke, but do try to keep your voice down.
Sorry, Professor. This place is just so impressive.
I understand the feeling. It's also quite large. Finding your future self in here may prove difficult.
Fortunately for us, we're not the only ones searching here...
Luke Triton, 23
And to say this other person is "searching" is a bit unfair. He's probably just been waiting for us the entire time...
He's the... future me?
Or rather... I suppose I should say it's nice to see you again.
I mentioned it in the intro, but it bears repeating. Future Luke here is voiced by Yuri Lowenthal.
He does an okay attempt at a British accent, but it's not really great. Sounds like he just kinda gives up and settles for whatever is basically close enough. I've certainly heard worse.
Suspicion
Um, hi, Professor. Oh, you're talking to him.
This is going to take some getting used to.
I can't believe how small I used to be.
Hey! I'm not that small!
So, tell me, why exactly did you go through such pains to bring us here?
I'll be happy to tell you in just a moment.
In this particular instance, I'd say this degree of skepticism would normally be fine.
Except we have Luke here with us as well, and surely Future Luke would recognise himself.
Who else would I be?
Allow me to explain.
In my London, it's rare to find someone who doesn't know the name Hershel Layton.
I think in Layton's London that would also be the case. He's not exactly a big unknown or anything.
Are you saying you think the professor is a fraud?!
Luke, please, let yourself finish.
As you know, he was a master of disguise.
How do I know the man before me now isn't Don Paolo in another of his costumes?
How that's just rubbish, and you know it!
Is it now? He's tricked us before. Who's to say he couldn't do it again?
He's not wrong! It was only about a year ago when Don Paolo pretended to be Flora for about half of the Diabolical Box. And he nearly pulled it off without issue!
Very well. I'll play along. How do you propose I prove my identity?
Silence
One thing I really like during this small animated scene is that Future Luke walks with the same posture that Layton does during his deduction scenes. And he even points directly in the exact same dramatic way. It's really subtle but really cool.
End
Puzzle Battle 
As a cautious man, I'm sure you have questions about my identity as well.
I therefore suggest that we each prove our identity to the other's satisfaction.
To this end, I propose that we demonstrate the power of our respective intellects.
Should you find the solution, I will give you the chance to present me with a similar challenge.
If I am who I say I am, I should have no trouble solving whatever you throw my way, should I?
Let's get started. Before us are four cards arranged according to the following set of conditions:
Second, a club is not next to a spade.
Finally, a heart is directly to the right of a club.
Using just these three conditions, I challenge you to find the spade amongst these four cards.
Puzzles Reinvented
1. Your task is to find all the routes that meet the conditions. Think about how each route crosses the central column of squares on the bridge.
Crossing four black squares and three white ones means you have to cross the bridge in seven moves, so you can't afford to backtrack.
2. Once you've worked out the pattern in the routes that work, just go ahead and count them one by one.
As Hint 1 mentioned, backtracking won't work. Keep the other conditions in mind and you should be fine.
Not too many puzzles to get through this time, really...
1. It's times like this that you'll find the Memo Function useful. Try writing on each square the directions you can move in.
If you write them down, you'll probably notice that squares with two or more arrows on them really restrict your movement options, especially since you can't go back to your original square.
1. Remember that each shape consists of the same capital letter and its reflection.
2. Cover either the right or left half of the shape, and try to draw in the other part of the letter. It might shed some light on the situation.
1. "Mr. 8:20" refers to something about the person's appearance.
2. Don't worry about what the people are wearing, because they can always change their clothes. No matter what time you see this person, it's 8:20...
1. Imagine yourself sitting at the table. Notice anything unusual.
2. Look closely at the two gentlemen playing cards. If people think that one has no idea what he's doing, he's probably doing something strange.
Puzzle Battle
There's no such thing as a hint for a puzzle battle. Don't be silly. You're on your own here. Better be able to live up to the Professor's title that's for sure. 