# Treasure Hunt Solutions

1. Oct 14, 2004

### Gokul43201

Staff Emeritus
Clue #1:

A word that you're looking for refers to the loci :
"Such points that never may be found in between."
Know that it refers to your fingers and your toes, but a
message it conveys is vital to crossing this step.
Ere it's mixet, when mixed, will tell you its form.

Discover the keyword that the above passage describes, and use that keyword to decipher the hidden message in the passage. And keep the keyword with you; you'll have to use it to get the next clue.

Solution #1 :

Keyword : EXTREMITIES
Explanation : Extremities are peripheral points (never found in between). The word also refers to parts of the body that are farthest from the heart, such as fingers and toes. If you jumble the letters of the phrase, Ere it's mixet, you get the word 'extremities'.

Hidden Message : Ask me in a PM
Explanation : If you look at the letters that make up the extremities of each line of the passage (going down the laft side and then the right) - the first and last letters of each line - it spells out the above message.

Extra Info : This type of cryptic poetry is known as an acrostic (in this case, a double acrostic), and was common during ancient times. The acrostic is believed to have been invented by a Greek comedic writer named Epicharmus, of the 5th century BC. Poe's Elizabeth is the only famous acrostic from modern times that I'm familiar with. There are probably many more.

Last edited: Oct 14, 2004
2. Oct 14, 2004

### Gokul43201

Staff Emeritus
Upon receiving a Private Message with the correct keyword, I revealed the second clue.

Clue #2 :

Qttp sty ns Sfyzwj, tw Xhnjshj, gzy rnsj.

To find out what type of cipher is used above, connect the following hints to a common theme: (this common theme is a keyword, save it for later)

(I) a hot time (not for the Kiwis, Swazilanders, those from the silver country, and other such types)
(II) Macduff’s unique qualification
(III) (I’m going to disguise this hint, lest it be a giveaway) blurrfinerdentoutsparmaninstead (What are the odds that you’ll crack that ?)

Solution #2 :

Keyword : The theme that connects the 3 hints is CAESAR.
Explanation :
(I) July is a hot time for people in the northern hemisphere (the exceptions listed are all from countries of the southern hemisphere). The month July is named after Julius Caesar.
(II)In Shakespeare's Macbeth, the three witches predict that Macbeth can not be killed by "any man, of woman born." Macduff was able to kill Macbeth, because he was not strictly "born" - he "was from his mother's womb / Untimely ripp'd" - he was delivered by Caesarean Section. Legend has it that Caesar himself was delivered this way - hence the name.
(III)If you extract the "odd" (starting from the first, every alternate) letters from this text, it reads (with spaces appropriately added) : buried not praised. This is a direct reference to Caesar, through the famous words of Shakespeare's Mark Anthony, who at Caesar's burial speech says "Friends, Romans, countrymen, lend me your ears; \ I come to bury Caesar, not to praise him."

Message : Having found the keyword, it is possible to decipher the coded message. A quick google search will reveal that the Caesar Cipher (or Caesar Shift Cipher) is the simplest form of mono-alphabetic substitution cipher. The original Caesar Shift worked by replacing every letter by a letter 3 places down. So A would be written as D; B as E, C as F, and so on. The shift that I employed was 21 (or -5). So replacing each letter with the letter 5 letters before it, the message becomes :

Look not at Nature, or Science, but mine.

Interpretation of Message : Notice that the words 'Nature' and 'Science' are capitalized. This suggests that they are implied in a sense other than the usual. In fact, 'Nature' and 'Science' are scientific journals of the highest repute. So the message is simply suggesting that you look at my journal to find the next clue.

Extra Info : Another cipher that was popularized by Caesar is what is known as a Scroll Cipher. A long, narrow, rectangular strip of parchment (or scroll) is wrapped around a cylinder of a specific diameter. The desired message is written in columns so that successive letters are found in successive turns of the scroll. To decipher the message, the recipient must possess a cylinder of the same diameter.

Consider the following message on a long scroll : TALRCEAERHSCOUNTLSICIFMCSELSRPCFENTOIOHIETITNSLERRHNEG.
Wrap this around the correct cylinder, and it will make 6 wraps as below :
Code (Text):
T  A  L  R  C  E  A  E  R
H  S  C  O  U  N  T  L  S
I  C  I  F  M  C  S  E  L
S  R  P  C  F  E  N  T  O
I  O  H  I  E  T  I  T  N
S  L  E  R  R  H  N  E  G
Read this vertically (column by column) to decipher it.

Last edited: Oct 14, 2004
3. Oct 14, 2004

### Gokul43201

Staff Emeritus
Clue #3 : Part A

Upon visiting my journal, one finds the single entry, stating :

"You're very close, but not really there yet...think about how you'd start to greet a Frenchman - that might help"

Solution : Some Frech greetings that come to mind are "Bonjour !", "Comment allez-vous ?", etc.

The second one seems promising as the journal page has a provision to leave comments.

Clue #3 : PART B

Visiting the comments, one comes upon the following strange comment left by a user called 'for3to0won' :

G : "Go to this quetion !"

U : "Which quetion ?"

G : "This, stupid !!"

U : "This ???? What's 'This' ?"

G : "Figure it out. AS*TO=THIS"

Solution : The next clue is located at post #1504 in the thread "Ask a stupid quetion...", found in the General Discussion forum.

Explanation : The intentional misspelling of the word 'question' is an obvious hint. This is reinforced by the word 'stupid' in the next line. The clue must be hidden in one of the stupid quetions...but which one ? That is addressed by solving the puzzle AS*TO=THIS, and going to the post refered to by the number representing THIS. In this puzzle, each letter represents a different number, with A and T <> 0.

There's two ways to solve this puzzle.

(i) Write a program to try all combinations and select the ones that match;

(ii) THIS is a 4-digit number. The total number of posts in the thread is less than 1600, so T=1. So, TO is a number between 12 and 19. Let's try each of these options keeping in mind that S*O==S (mod10).
With O=2, this condition is satisfied only by S=0. But TO = 12 => AS > 83, so the only possibility is 90. But 90*12=1080, which is not allowed as this makes H=S. This takes longer to write up than actually do. With O=3, you have S=(0,5), with O = 4 and 5, only S=0 is possible and for O=6, S=(0,4). Going this way, the 15th possibility works, giving TO = 16, AS = 94 and THIS = 1504.

That's not too many numbers to try, is it ?

Extra Info : The only non-high school math (though it's simple enough to be) used here is a number theory technique known as modular arithmetic, or the arithmetic of congruences. Most of the properties of congruences were developed by Gauss when he was still a teenager !

Last edited: Oct 14, 2004
4. Oct 14, 2004

### Gokul43201

Staff Emeritus
Clue #4 : Part A

The clue hidden in the "stupid quetion..." thread, post #1504 reads :

Find out more about for 3 to 0 won

Solution : This is a direct reference to the member (for3to0won) that provided the previous clue as a comment in my journal. Checking for3to0won's profile reveals the following :

Biography: practising LaTeX

Occupation: doing homework

Checking for3to0won's posts shows that he has a post in the Homework Help sub-forum. The content of this post is quite curious :

Clue #4 : Part B

It is good to practise LaTeX. Many maths symbols and Greek characters can be written :
$$\tau\upsilon\rho\nu\beta\alpha\chi\kappa\sigma\iota\gamma\alpha\nu\delta\epsilon\lambda\iota\mu\iota\nu\alpha\tau\epsilon\tau\eta\epsilon\rho\epsilon\pi\epsilon\alpha\tau\iota\nu\gamma\kappa\epsilon\psi$$

Surely this is the clue !! It looks like the first line is merely an excuse to explain the somewhat enigmatic second line...but it connects to the entry in the profile !

Solution : The message revealed by the Greek characters is "turn back sig and eliminate the repeating key." This is now clue #5.

Explanation : This too is a mono-alphabetic substitution cipher, but made all the more simple by using Greek letters that are equivalent to English ones.

So, $\tau-\upsilon-\rho-\nu$ = tau-upsilon-rho-nu represents t-u-r-n. And the rest follows.

Extra Info : The story of the decipherment (by Ventris, Chadwick and others) of an Ancient Minoan script refered to as Linear B, found on tablets in Crete makes for an interesting read....if you're into that kind of thing.

Last edited: Oct 14, 2004
5. Oct 14, 2004

### Gokul43201

Staff Emeritus
Clue #5 :

As revealed above, this clue reads : turn back sig and eliminate the repeating key.

Solution : Doing this reveals : "if u factor hardy’s cab#, the unlucky one is the _ _ of the others". This is now clue #6.

Explanation : Clearly, 'sig' is a reference to my signature, which at the time (I've changed it since) read :

srreahtosehetfaoc_ _rehatsiseneaoyckrculanuesht,# beaaccrsa'ysderahacrortcaasefaufci

The first thing to do is to turn this back (or reverse it). That gives :

icfuafesaactrorcaharedsy’asrccaaeb#,thseunalucrkcyoaenesistaher_ _coaftehesothaerrs

The next thing is to eliminate recurrences of the key. Now the only unused key, at this point is CAESAR. Looking closely at the message text reveals the word appearing repeatedly, though interspersed, throughout it :

icfuafesaactrorcaharedsy’asrccaaeb#,thseunalucrkcyoaenesistaher_ _coaftehesothaerrs

Removing all occurances of this word, gives :

ifufactorhardy’scab#,theunluckyoneisthe_ _oftheothers

And putting in the correct spaces gives the required solution.

Extra Info : In cryptography, characters introduced into the text (which have no relevance to the message, much like the repetition of "caesar" in the above case) to confuse the unwanted reader, are known as nulls or dummy letters. Francis Bacon, himself an amateur cryptanalyst, liked to call these letters insignificants.

6. Oct 14, 2004

### Gokul43201

Staff Emeritus
Clue #6 : Final Clue

As revealed above, this reads : if u factor hardy’s cab#, the unlucky one is the _ _ of the others

Solution : the words that fill the blanks are : arithmetic mean

Explanation : "Hardy's cab #" refers to the number 1729, made famous by the mathematician Ramanujan (see Extra Info for details of anecdote).

Factoring this number into its prime factors gives : 1729 = 7*13*19. So, these are its three factors.

Clearly, the "unlucky one" is 13, (from the common superstition that 13 is an unlucky number)

So, the problem to be solved is "13 is the __ __ of 7 and 19". The most obvious answer is "arithmetic mean" since 13 = (7+19)/2.

Extra Info : Riding a taxi from London, (on his way to visit Ramanujan at the hospital) Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, "rather a dull number," adding that he hoped that wasn't a bad omen. "No, Hardy," said Ramanujan, "it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways."

$$1729=1^3+12^3=9^3+10^3$$

1729 has since become known as the Hardy-Ramanujan Number, even though this feature of 1729 was known more than 300 years before Ramanujan. And numbers of its type (the smallest numbers expressible as the sum of 2 cubes in n ways) are sometimes called Taxicab Numbers.

Last edited: Oct 14, 2004
7. Oct 14, 2004

### Gokul43201

Staff Emeritus
Epilogue :

Having arrived at the solution "arithmetic mean" and finding nothing else to do, one might do a search in PF for this phrase, and will find a thread started by me, with this title. The only post in this thread reads (in white, as usual) :

Well done, brave adventurer ! This is THE END, my friend.

Thanks for playing. Hope you enjoyed the game !

And that's the end of the solutions !

Now would be the time to object, clarify, criticize, ignore or whatever else you wish.

8. Oct 14, 2004

### TenaliRaman

Nicely done!
(And sincere appraisal this .. Monsieur!)

I was pretty dumb in not seeing through buried and praised clue .... given that the other two were crystal clear .... and as usual i was barking up the wrong palm tree ...

Prolly the reason was it reminded me of the game ..
A game where a narrator sets up a crime scenario. Others have to ask question to the narrator and he answers them suitably .... The objective was to figure out how the crime took place ... (You see in these games one has to go outside the box and i went a bit too far with this one :tongue2: )

Anyways ,
still a great game and highly enjoyed one at that!!

-- AI