You now know where your wife is, so you hop on a plane and fly over to France. You reach the house and burst through the front door, only to find the house deserted. In despair, you slump into a chair in the kitchen. You then notice a note pinned to the table in front of you:
To xxxxx,
/
Now it seems you misunderstood me, despite my letters to you. I don’t need any help, although I’m happy you came. I told you to please not come looking, but it appears you have anyway. Honestly, again, you have to return.
I’ve been forced to disappear. You must go back to the family to make them see. Make sure you check on the kids, and do not forget, before going home.
Care for my family. This will not be easy for them to take. Tell them I was hiding after being afraid someone was coming, and that I ran. I was scared, but over time the fear reduced and I became less and less cautious so I then left my carers when things got out of hand. When I heard you were coming to find me before trying to save me I had to return to them and to hiding. We couldn’t afford to meet.
Enough of that, I don’t have much more time to write each of these letters. This, with life having gone into reverse, I expect will be my last letter to you. But I hope that sometime I can, you have my word, come back.
Think of me often and hope our next meeting is soon. Our relationship was just absolutely unimaginable, the best possible, I thank you a lot for that of course. I really am extremely thankful, our life was first class and fantastic.
Really must hurry now, can’t say the reason why but I really have to go. To be truthful there’s so much more I want to say to you but I can’t, for one thing that’s straight forward - my dinner’s going cold. So’s my tea.
You can move but will always, and hopefully one day once again can be my husband, you know that already without these words. Remember I love you. This is one of, or the hardest thing I probably have ever done, I’m short of breath, trying not to get tear drops over these letters, or even worst and the very thing I want last, over my writing. It’s really hard not to sob.
\
Love from me,
Lucida Xavier
Realising that your wife may be here after all you get up and look in the next room to find a page of what appears to be algebra. You also put it in a spreadsheet so its easier to look at, though the formating isn't as good.
Expecting more, you go upstairs and find a page ripped from a book. You take a glance at it. It seems to be from Great Expectations by Charles Dickens, but you suspect the letters themselves are more important than the book...
And lastly you find a load of supposingly meaningless letters scrawled on the wall upstairs. You write them down:
Smi semo dllam olive sr etirp,
Mohw wdegre dhti regna.
Ttub wsginh nere ato thgirl.
Inehw dt ndi tto onru ff.
Syeht sdia agnihtemo ltuob gninrae,
Aro lt stsae sgnihtemo tralimi to tah,
Tmi bdeppar atu tosl keh ye.
That appears to be it. You sit down and think hard about what these could mean.
Can you save your wife?
If you wish to see how this story ends, see the epilogue at the end of the complete answer. However the answer and epilogue contain spoilers.
Answer
This is a comprehensive and complete roundup of the answers submitted by various users and brought together by the OP. A lot of this was solved in chat, mainly by Deusovi, Rubio, Techidiot and Volatility.
The first letters of each paragraph say 'NICE TRY'. So we need to look somewhere else...
The italics say 'check the last letters', so looking at the last letters of each paragraph, from bottom to top, you get 'BACK TEN'.
Going back, counting ten words each time like we counted forward nine in save your wife, and starting from the last word of the last paragraph you get the message:"Last letters of the words can move forward to be the first of the next word, but reverse each of them before hand. I fear that I will not see you again. Please help me."
This seems to point towards the supposedly 'meaningless' letters. By reversing each word and then moving the last letter of each word forward you get the riddle:
'I'm some small devil or sprite,
who merged with danger.
But things were not alright.
When it did not turn off.
They said something about learning,
or at least something similar to that,
I'm trapped but also the key.'
The answer to this is
IMPRISONED
Because
An 'IMP' is a small devil or sprite
A 'RISK' is a danger
Take away 'K' to get 'RIS' because things were not alright (OK)
'ON' is the opposite of off, and 'it did not turn off' 'ED' stands for education which is a synonym of learning
IMP+RIS+ON+ED = IMPRISONED
'IMPRISONED' means trapped and 'key' suggests a vigenere cipher.
Each algebraic equation:
can be simplified. For instance, the first one - '$2P + 3N - P - 2N + 3E$ - can be simplified to $1P + 1N + 3E$. These are actually directions from a compass.
$1P$ means the P in the first paragraph of the book. There is only one - it's in 'upon'. In each simplified equation, there is only one in the paragraph of the first letter. Using the example of the simplified one above:
$1N$ means go 1 letter North
$3E$ means go 3 letters East
Doing this we get the letter 'O' in 'your'.We should also note that 4 equations give the words 'SPACE', 'GAP, 'VOID' and 'BLANK' when simplified which suggest a space in a sentence.
The number and the letter at the start of each equation are the paragraph number and the letter in it which is the only one. The rest are directions, but it is important to simplify so that the letters are in the order they appear in the equation because $3E+3N$ won't be the same as $3N+3E$ due to letters not being exactly above each other and different width letters.
Doing this for every equation gives:
The phrase 'oa abfos.wtj aaamm fizfhze ansXv.jpg'. The 'C' in the 29th equation indicates capitalisation. If you want to see each simplified equation and the letter it maps to, there is a spreadsheet created by Deusovi and edited by others (especially Rubio) with all the information. (Thanks to them for that.)
So
http://i.stack.imgur.com/ansXv.jpg is a valid imgur link and gives:
Transcribed this is
1-4-4 24-24-9 9 22-9 24-24-9-9 24-12-9
This when changed to letters is:
Add XXI I VI XXII XLI
And changing Roman Numerals to base 10 gives:
Add 21 1 6 22 41
If we use
IMPRISONED as a Vigenere key we get
Go lkxwe.jpg solve numbers
http://i.stack.imgur.com/lkxwe.jpg is a valid imgur link but just gives a torn piece of paper:
However
If you add the numbers given to each letter of the imgur link, you get a new letter, and that gives the final image of https://i.stack.imgur.com/gldst.jpg:
EPILOGUE FROM OP:
Realizing where your wife is, you scrabble around on the floor. There must be a trapdoor somewhere as you've already checked every room. You eventually find it hidden under a rug. Lifting the trapdoor up reveals a flight of stairs leading down to a door. It is locked on the outside. You scramble inside and find your wife gagged against the wall. You untie her and she falls tearfully into your arms. After all that effort, you're finally reunited with your wife. You both found her and saved her.
You solved the puzzle...
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