"Bon Bon! BON BON!"
Bon Bon massaged her sore head, nursing a thumping headache over the strongest coffee she could make that morning. She was wearing her pale blue nightgown and was sitting at the breakfast table, enjoying the peace and quiet, until her housemate, Lyra Heartstrings, came jumping down the stairs in giddy excitement, clutching what appeared to be yesterday's paper in her hooves. "I did it, I did it!"
Bon Bon sighed. "I swear to Celestia if your petition to turn all the benches in Ponyville into reclining massage chairs got passed by City Hall..."
"Not that!" Lyra shoved the paper straight into her friend's annoyed face. "Did you read that article yesterday? About that eccentric billionaire?"
"Hmm? Oh, that guy? That guy who said he'd give his fortune to the first pony to submit the correct answer to a puzzle he had held on to since birth?"
"That's him, that's him!" Lyra nodded quickly, her grin never leaving her face. "Well, GUESS what happened?"
"...I dread to ask, but you solved it?"
"I SOLVED IT!" Lyra shouted excitedly. "All by myself! Fame and fortune call to me! The riches are mine for the claiming!"
"Lyra, be reasonable," protested Bon Bon. "As far as I remember, it was just a three-colour map puzzle: one of those ones where you have to colour in parts where no two matching colours touch. It was hardly the most mind-blowing riddle of the ages here. Somepony's probably already submitted the answer and is enjoying their new riches right about now."
"I think not!" Lyra protested back. "he said you have to turn up to his residence with the answer before you get the money, and it's so far out that NOPONY could ever get there on their own!"
"Including you," Bon Bon pointed out.
"Nuh-uh! I'm heading to the bank to borrow the cash for the trip. By the time I'm back we'll be rolling in it! Wish me luck!"
"Wait, aren't you going to have breakfast..." Bon Bon began to say, before Lyra zoomed out of the house and slammed the door on the way out. "...first?"
She looked down at her coffee. "This isn't strong enough for the morning anymore. I just know it."
-
"Miss Heartstrings, I can't just loan 10,000 bits to you without you explaining WHY," Tender Lender, Ponyville's bank manager, sighed in frustration. It had been a difficult start to the morning. First, minutes before she was about to open the bank, she spotted a green unicorn hammering away at the doors of the building, demanding entrance and swift vengeance to all who would deny her, before she was made to sit and wait for 8 am like a civilised pony. As soon as the clock struck eight, she promptly galloped inside and demanded a loan of 10,000 bits to Tender Lender's face.
"I told you, it's so I can make a trip to an eccentric billionaire's secret hideout so I can claim my reward of 10 million bits for solving a puzzle in the morning newspaper!" Lyra threw up her hooves in frustration.
"Well..." Tender Lender pushed her glasses up, trying to regain her composure. "My congratulations, i suppose." She pointed to the piece of paper Lyra was clutching in her hoof. "Forgive me, but is that the puzzle there?"
"Yes. And no, you can't look at it."
"Miss, I am not prepared to give out a loan you may not be able to pay back. You are relying entirely on yourself receiving this 'reward' of yours to pay back the interest." She reached out her hoof. "Can I at least confirm it's solved? So that you don't spend a wasted trip?"
And so Lyra had hit an impasse. Simply showing the solution to Tender Lender wouldn't do: her rampant paranoia made her afraid she would simply kick Lyra out of the bank and take the reward for herself. She briefly toyed with the idea of varying degrees of bodily harm or threats, but decided that the thought of needing to pay for all legal fees plus her distrust of those in the legal profession soon put a stop to that.
In fact, Lyra felt that in order to minimise attention, she needed to keep this between herself and Tender Lender. Nopony else was to know. No media outlets, no lawyers, no middleponies, and especially no turning for help to convince the poor bank manager.
She decided that if there was any time to prove her worth as a puzzle solver worthy of such a fortune, this was surely it.
Well, this is a good one
science has proven that a 4 color planar map(the official name for the problem) is ALWAYS possible, but 3 colors is tougher to explain
As long as no area of the map touches 3 other areas that dont touch themselves, then it should be possible
Why are you looking suspiciously at me?
And how far away is it that she needs that much cash?!
Also, the obvious answer is to rob the bank. Once she's rich she can pay the guy back and pay off a lawyer to clear her of all charges. Or at least, that's the idea, but it turns out like a few dozen people already solved the puzzle, had the exact same idea, and they're already there clamoring for the money and poor Lyra gets nothing.
9245898
And that's why I added the clause of 'nopony else is to get involved'. Because I knew this was how you'd answer.
9245932
She can rob the bank without getting anyone involved! Just wait until they close or nopony's looking.
9246026
Others are involved the moment legal actions are needed
9246048
Oh
Simple. Just hold it up to the light for a brief moment so he can see that the conditions are fulfilled but he can't remember exactly how it went.
Ta DA!
9246026
Then that technically counts as a burglary, for all legal purposes. For it to constitute a robbery, it needs to involve the threatening of one or more victims.
9246431
Thaaaaaaaaaat's one way...but assume I want it solved mathematically.
9246781
It says logic puzzles in the title. Not math puzzles.
Can we give the bank an unsolved copy of the puzzle?
Cause if not i have no clue how to word it, but i did find the proof
https://www.sciencedirect.com/science/article/pii/S009589560300025X
It is similar to how Penn and Teller tell the performing magician what, they think, the secret is without revealing said secret . The only difference is, Tender Lender doesn't know the solution...
What can only those, who know the solution, show ? If Lyra didn't know the answer, she could never give an example (because there are bound to be several different ways of colouring the map), but she does know and can give one. So she should just colour the map, and then again and again... "Anything you give me I can solve!" -- she might claim. I do believe, it is convincing enough .