Oh Zacharie you are such a simple soul that is soo easy a mere exercise in Interlocking circles.
To find the area of the asymmetric "lens" in which the circles intersect, simply use the formula for the circular segment of radius R^' and triangular height d^'

And because it is a simple farmer he can use unit discs in which case in order for half the area of two unit disks (R=1) to overlap, set A=piR^2/2=pi/2 in the above equation .
But a simple farmer would run rings around you for he knows that a goat will eat through a rope tether very quickly so he will need to fence his pasture to exercise pature rotation.
We will be going into an unexplored tunnel very soon but first I need to treat this injury to my hand.
I suppose you were given that question by Yves Leterme wanting to know how to pasture his favorite goats, named Trudy en Vicky
Battery Status 60%

 

Zach had been watching closely while Blue was writing the solution. She didn't really care who this man really was, as she had no choice whether she had to get along with him to get out of this place. In all modesty she had to admit that in fact she didn't know the solution to this riddle herself - some would call her a simple soul - but she had other ways to check about Blue's honesty. When he handed her back Mr. Phonie, she quickly ran a scan over what he had written. While searching for the riddle earlier, she had launched a 'style recognition' program, which analyses the way of writing of an individual. This one came out with a flag! The frequent use of the words 'simple/simply' and 'easy', combined with the multiple 'lol' smileys, could only come from a twisted mind of a genius. Who else knows about goats eating ropes and formula for interlocking circles?

'Well?' said Blue, 'satisfied?' She nodded... 'Just one last thing, before we go', she replied, 'I noticed the chain of my bicycle got stuck and fell off my front gear... Could you also show you are a gentleman and fix that for me?'

Of course he could do that. Quickly Blue turned the bicycle upside down, and while whispering softly a song that was just loud enough to hear the words 'simple' and "easy', he put the chain back on track, and gave a quick turn on one of the pedals... Ouch! He forgot about the other pedal... Of course it also moved and hit him in the face like a piece of rock. At the same time he forgot to take away his hand and it got stuck between the chain and the front gear...

That's how Shocking Blue injured his hand. Lucky there was a woman in the room, and after some treatment - the hand (the face was a mess for ever) - they were finally ready to go.

Battery Status 50%

Blue said "right meet me in the garden cave, I have some other things to do", and strode off thinking "Clumsy female turning that back wheel without warning , still I will do a proper job of treating my hand later."
Pedalling as fast as she could Zach cycled through to the power room where she boost charged Mr Phonie, checking she still could not get a signal so she cut back to the map room, went through the central cave and into the garden where she hid herself and bike behind some fruit bushes. Strange she thought there was no sign of Shocking Blue in the map room.
Suddenly she felt a prickly sensation on the back of her neck as if she was being watched. Spinning round she could see nothing but then in her peripheral vision she saw the soil moving just 2 metres to her left. When she turned her head that way there was Blue. How had he got there without her seeing or hearing him?
"Right said Blue, "Next destination the unexplored passage over there, you may get your proof."
Off he went with Zach struggling to catch up after walking down the tunnel for a few hundred metres she suddenly felt disoriented and dizzy as if the world had shifted and closed her eyes. When the dizziness had passed she opened her eyes again to realise that she was in bright sunlight. Turning round there was no sign of the tunnel just a cliff face.
"Come on, stop dawdling" said Blue and off he went again down a track. Following in his footsteps like a little scared puppy they turned a corner and Zach saw
She heard a clock a long way away strike 12
and a little further on at the side of the track was a big sign with a map

"Just where are we and how did we get here?" Zach demanded.
"Ok" said Blue. " For over a century people have been disappearing when they became inconvenient or had information that was wanted. Some returned but were changed in subtle ways or they may have been clones. Only two people have ever really escaped from here, one was well shall we say a consulting detective who was captured after he left the Reichenbachfall and although he recorded the account in his archives he told his scribbling doctor friend that he had been in Tibet. The second was well you don't need to know who that was but he thought he had destroyed the place and caused a television series to be made called "The Prisoner" and shown in 1967. You asked for proof ,well you are about to get it. Now excuse me for a moment I need to change."
Saying that he walked behind a large boulder and re emerged a few moments later in totally different clothes and with a different face.
"Blue? Is that you? " asked Zach . "Well how many other people have you injured with a bike chain" was the reply as he held up his hand.
Just then there was a roaring noise a bit like an elephant cry and a 2 metre white balloon bounded up the track stopping just behind Blue.
Behind it came a portly man with a beard wearing a badge showing a weird penny farthing bike with the no 2 on it. He was accompanied by 6 tough looking ruffians all wearing striped sailor -shirts.
"Welcome back Number 6" said the bearded man. "You won't escape this time , here is your number badge". Blue took the badge and threw it away saying "I will not be pushed, filed, stamped, indexed, briefed, debriefed or numbered. My life is my own. " "We will see, you know you own way back to your house" said No2.
Turning to Zach he told her to come with him although she had little choice as she was frogmarched to his office in the Green Dome.
"You are number 66" said Two.
Number66: Where am I?
Number 2: In the Village.
Number 66: What do you want?
Number 2: We want information about Number 6.
Number 66: Oh you mean Blue, whose side are you on?
Number 2: That would be telling. We want information... information... information.
Number 66: You won't get it.
Number 2: By hook or by crook, we will.
Number 66: Who are you?
Number 2: The new Number 2.
Number 66: Who is Number 1?
Number 2: You are Number 66.
Eventually she was released after being taken to a curious dwelling she was told was her new home.
Zach decided to explore and looking at her map made her way to the cafe in the hope of getting a coffee and fries. Reaching it she saw Blue relaxing with a coffee and watching 2 seagulls on the roof.
Sitting herself down at his table she said "I want answers, firstly how did you change your appearance and clothes so quickly ?"
Blue replied " As an old Celtic friend of mine used to say Si tibi narrarem, te interficere deberem."
"How do we get out of this crazy place" was Zach's next question
"Look at those seagulls on the roof and that strange cloud going across the sky" was the reply.
Just then the own clock struck 5 and blue got up & said "Same time same place tomorrow, Be seeing You"
Zach woke late the next morning having had a surreal dream that she was a saloon girl in a wild west town called Harmony and they were trying to make Blue become the Sherriff.
She went to the cafe again just before 5 and again joined Blue.
"Look at those seagulls on the roof and that strange cloud going across the sky" he said again just as she was watching the clock struck 5 again.
"How is this going to help us get out of here? " she said
Blue replied "I suppose it is pointless to ask if you can calculate Noetherian rings of infinite Krull dimension" and seeing the blank look on Zach's face continued You should have observed that we are in a time loop a mobius strip of time, that being the case it should be obvious how we escape. I will see you at the correct location tomorrow, be seeing you".
That night Zach dreamt that she was the daughter of a crazy professor and kept trying to find ways to kill Blue.
The following morning she thought long and hard about Blue's final answer.
As Zach wanders around in a multi coloured cape twirling a golf umbrella and prancing to the Radetsky March has she forgotten all about Mr. Phonie & can she solve Blue's paradox riddle? Or is she just an airhead? Have they already brainwashed her or was there not enough brain to wash
Battery Status 40%

That night Zach dreamed she was sailing again. She wasn't sure she was on a boat, but she saw Blue wearing a captain's hat, shouting orders in some kind of microphone with a loose end wire. She couldn't tell for sure if it was Blue appearing in her dream again, or the wavy movement of the water that made her feel like seasick, but she was about to throw up when a rough hand on her mouth woke her up. A whispering voice told her to 'be quiet' as he 'didn't mean no harm to her', to 'get up and dress'. She obeyed - wondering what made her so confident - and then she recognized the man who woke her up... It was the captain of that cruise ship she had been aboard when it perished. 'Miss Zach' he said 'please don't ask questions, just follow me. I know a way out of here.' They left trough the back door, and the captain lead her on a narrow path to the coastline. There they boarded a small boat and off they where, towards the open sea. Zach had been quietly following like in a trance, wondering if she was still dreaming, but once she felt the cold and salty water drops on her lips, she realized this could really be happening. The coastline disappeared and soon they were surrounded by a deep mist, when appeared the silhouette of a modern yacht, where she saw people waiting to throw them a rope. A few moments later they were aboard the yacht and she heard the captain yell some orders for a quick departure. She found a moment to talk to the man... 'Sir?' she wondered, 'how do you think to get away from this? Aren't we trapped in some kind of time loop here, and supposed to solve this mobius riddle first?'. The captain kept his eyes on the map, while adjusting some number readout on a spinning wheel, 'well, Miss Zacharie, what about having Mr. Blue solve his riddle himself? We've reversed the mechanism of the only clock on the Island, that way bring you back where you were lost.' Then he yelled in some kind of megaphone: 'Full power straight ahead, gentlemen, destination... the Bermuda triangle!'. Zach replied 'the Bermuda triangle? Are you kidding? That's not where we came from!' 'Maybe not, indeed', the captain replied, 'but it's the only way to get there. Trust me, I know what I'm doing...'. Then he turned to her, 'and bytheway, I think this one belongs to you' and handed her over a mobile phone, which she immediately recognized as Mr. Phonie. 'I found it where you left, and it still appears fully charged...' Zach took Mr. Phonie in her hands, switched it on, and a big smiling smiley appeared on the screen... For a moment Zach felt as if this mobile was happy to see her again, and - if she was really honest - she felt a bit like that too...

Battery Status 100%

In the meantime, Blue was sitting again - alone this time (one can't deny his destiny) - in the cafe, relaxing with a coffee and watching 2 seagulls on the roof. And although it wasn't the way he expected the riddle to get solved, and despite of his evil and twisted mind, he had to admit that devilish woman escaped, and left him feeling a little foolish... Now he had indeed to solve this riddle himself to get out, that way find her back in the caves, to continue their descent... (In case he forgot this was what the chapter is about... )


Battery Status 90%

Next day, Zacharie received a message from Blue: 'Hi, Zach, Blue here. Where are you? Did you leave the Island? But how? Damn you, Zach! This has never happened... Nobody escapes the Island! The only way out is trough the local hospital. I had to throw myself of the cliffs to get admitted there. They treated me well, but I am presently full of painkillers. I managed to make it to the RX room, that in fact is a port to the outside world. I made it back to the caves. My hidden camp in the garden, remember? Earlier I have been checking those cages we saw on the map. I discovered some people who are kept captive. Most of them are indeed world leaders and other VIPs that have been replaced by clones. This is huge, Zach. I hate to say this but I really need you here to find a way out. But before all, be careful who you talk to and watch out for the people around you. They could all be fake. Machines looking like normal people, put in place with a purpose. Walking bombs, Zach. One of the prisoners showed me the way to the 'operation room' - it's the room marked with a '?' mark on the map - and I was able to have a brief look at what's happening there. It's ingenious - and sure to complicated for you to understand - but there's something interesting I noticed, that might be useful to you: all clones (robots) have a central memory that gets updated with latest data the moment they get released in the real world, replacing their captured originals. For that update they need a connection to the main computer. The connection goes trough a mini-USB port, located under the tongue of the clone. I suppose they prefer the wired transfer above wireless for discretion. I know, 'under the tongue' is not an easy place to check, but as far as I could conclude, it's the only way we have to distinguish the clones from the 'originals'. I'm not sure what power these 'clones' use, and if the same port is eventually used to 'charge' their batteries or something. I also discovered they are not equipped with a digestive system, so they obviously don't eat. Meaning, if you suspect someone skipping dinner for a cheap reason, don't think to fast it's a vampire... (Haha!) Oops... I'm sorry, just trying to keep the spirit high here. Seriously, may I advice to be very careful, and keep an eye on the people around you. Especially on people in charge. I have no idea where you are at the moment, but I saw your phone is online again, so I presume you're in the open and free. Hope to see you soon. Take care...'

Zach secured the message, and switched Mr. Phonie off to put it away. That same moment, the screen jumped back to life, and Zach saw another message appear, word by word, as is someone was writing them while she was reading... The message said: 'Zach, darling, forgive me interfering your business, but you are in danger. This might sound weird, but I've been able to connect wireless to this ship's computer. Reading previous message from your friend Blue - you should be more careful when choosing your friends, dear - I've thought if there should be any clones on board of this ship, they eventually need be updated by their headquarters. We haven't seen any postman since we boarded, so I suppose they get their instructions trough that USB port while connecting to the computer. I managed to install some tracking software and found out indeed there's at least one clone on this ship that made an active connection. Whether it's the Captain or someone else, I don't know yet, but I know it's the Captain's login and password that were used. I advice caution and closer watch of staff people of the boat. If we can find out who is in fact a 'machine', we might need to trigger it to establish connection again. Then I will be able to penetrate his system and leave some software behind, that will allow us to take control of the clone. Judging on previous message from Blue, I advice to be very careful, as these people look very serious about their case. If you need me, just tap the screen... I'm always there. Just keep me charged, will you?
You've got a friend. Mr. Phonie.'

As soon as the last word appeared, the message began to fade, and soon there was nothing left but a black screen. Overwhelmed by what just happened, Zach turned off the phone again. What was this all about? After a moment of thoughts, she decided it was time for action...


Battery Status 80%

Exactly that same moment, someone - or something - else decided to put into action his twisted mind, and the boat engines died... Zach jumped out of her cabin, and nearly crashed into the captain, who apologized and intended to resume his hurry to - what it appeared to be - the cause of the engines shutdown. Not so fast! - Zach thought - 'what's happening, Sir?' The captain turned around and replied with an apology: 'Nothing to worry about, milady, I'm afraid we're out of energy, and we'll have to wait a couple of days for the power to build up again...'

What's that supposed to mean? - Zach thought - 'Build up again' makes me think of an old Frankenstein movie, where the evil Doctor had to wait for a lightning to build up enough power to kick the monster to life. Aren't they on fuel generated power? Still at medieval level? She remembered rumors about fat bottomed bicycle riders being hold hostage to ride on static bikes to generate the power for the opening ceremony at the Olympic Games back in the old country. Maybe they have some spare riders locked in the ship's basement, producing power for the ship. What if this ship contained the whole English bicycle team, while their clones were competing in London? No wonder the power dropped just a minute ago: the cycling people downstairs probably just heard that Englishman won Gold at the Olympics. Soon other medals would follow... obviously prove these bicycle racers are not really human... And what about that swimming bot out there? The others fear him so much they simply pee in their trunks when he appears... Hence the water turning yellow lately.

While Zach was wondering if a doped swimmer peeing into the water would cause the other swimmers also to show positive when controlled for forbidden substances, she decided to have a look in the ship's basement...


Battery Status 70%