# 3 Step Puzzle with Increasing Ardor

#1 ________
#2 ________
#3 ________

Step 1: Note that something is missing in this puzzle and determine what it is (you may have to use it to realize it's gone). When you notice what it is, write it out in blank #1. You will surely agree that there is something impeccable about this missing thing. That ideal quality is the key.

Step 2: 8303765625 13841287201 X 531441 387420489 403.428793493 These numbers also seem to have some mysterious power hidden in them, the quality located above is the key to determining this power. Concerning the value X, when you have deciphered the numbers, you should realize that there are only two options; order them intuitively and choose the one that precedes the other. Using these values, locate their purpose and write it out in blank #2.

Step 3: 340 315 1103 These will be the hardest numbers to understand. Where the numbers in Step 2 derived their power, these numbers get a paltry structure. Using Step 1's quality as the key, unlock the secrets in these numbers. You will have to be guided by intuition and knowledge hence; It will be hard! In the event that you think you are at the decrypted end and still can't make heads or tails, just ask 245 335 310 what it means and that should make it crystal clear. Take the second part to this answer and place it in blank #3.

Ready? Bring me back the result that you ultimately determine and explain the procedure and you will receive my acceptance and praise! Please ask below in the event that you need help, and I will answer within reason. I recommend adding partial answers as this has many parts and using others' knowledge as a resource would be a great idea.

It has been a while, so I will add a hint to those entrenched in Step 2:

There are two numbers that may help to understand the meaning in the hidden numbers discovered in this step: 167 and 39. These numbers are not encoded the same way that the others are; 6 is not the key to understanding their value, but 256 instead (though it was originally only 128).

• I can't seem to figure out the formatting on blanks (made of underscores). Is there an escape character I should be using? Jul 14 '15 at 22:23
• Is that what you wanted?
– Bob
Jul 14 '15 at 22:58
• Yes, thank you Bob. For future reference, how did you do it? Jul 14 '15 at 23:16
• Clicking edit and seeing how it's done is easiest. Looking at the edit history you can see other stuff I tried first,
– Bob
Jul 14 '15 at 23:31
• I know what the first blank is, but I don't know what makes it impeccable... Jul 15 '15 at 4:46

The missing thing is

the letter F (while all the other letters are there somewhere).

Also, we all know that

F is the 6th letter (and 6 is the first perfect number, hence the "impeccable quality" about it), so that number is the key to determine the "hidden power" in step 2 as in Len's answer.

More to follow in a while, hopefully.

• Nicely done! Keep up the good work Jul 15 '15 at 10:09

I am pretty sure I understand part 2.

The hint mentions numbers 167 and 39, saying 256 is key, but it used to be 128. This refers to ASCII codes, and 167 and 39 are a top-aligned circle and the apostrophe, which look like degree and minute symbols. So we have 45 49 X 9 27 E, this being degrees and minutes. Clearly the E stands for "east" as in longitude, so X stands for latitude and can be either N or S. I assume N is the right answer, as the location on the south hemisphere is in the water, while the northern one is near Milan, Italy, and you also generally say "north and south".

• You're soo very close. And as a head's up, I verified the location of these numbers by entering directly into Google. Jul 15 '15 at 17:50

Partial answer for Step 2. All of these numbers can be:

reduced by the "mysterious power" of 1/6 as follows:
 8303765625 => 45 13841287201 => 49 X => ?? 531441 => 9 387420489 => 27 403.428793493 => 2.718281828 or $e$

These results look like OEIS sequence A069069. That is all I have for now.

• You are on the right track; the recognition of e will be very useful in determining the value of X. Jul 15 '15 at 10:13
• Is the order in which the numbers are given relevant? Jul 15 '15 at 12:12
• Incredibly so, I would say. Jul 15 '15 at 14:23
• I realized that my above comment may have been misleading; @Len your analysis of the numbers' hidden power was right on the money. Your last remark about the sequence, however, was quite far from the truth. Remember, be sure to cooperate with one another, you'll never find the answer if you don't work together! Jul 15 '15 at 14:27

I think I know #1. Is it

QUESTION.

There is no question asked in the entire puzzle. And usually when solving a puzzle, we tend to mentally ask ourselves, "What is the question here?" thereby asking a question, hence realizing what is missing.

• While a nice point and great explanation, this is not the key missing thing. I will update the post the resolve this coincidence. Jul 14 '15 at 23:48

Pretty sure I have the first transformation for Part 3:

The hint mentions these numbers having a 'paltry structure' where the numbers in Part 2 had 'power'. This could be referring to a base, in which case we can assume these numbers are represented in base 6. Translating them to base 10 gives us: 132 119 255. The presence of 255 makes me think these should be translated to hex, but that's about all I have at the moment.

And I think the correct answer for Part 2 may be:

Via Roma, 4. At least that's what I got when I typed in the coordinates from svinja's answer into Google Maps.

• Yep, I thought that too, and I'm stuck there too at the moment. Jul 16 '15 at 15:39
• Very nicely done so far! You are right on track. As for the second part, when I type the coordinates 45°49′N 9°27′E into Google, I get an address in a 4-letter city (more like small comune) in Italy; I got these coordinates from the Wikipedia page on this location Jul 16 '15 at 15:40
• Then would that make the answer for part 2: Erve Jul 16 '15 at 15:46
• Yes it would (needcharacterstopost) Jul 16 '15 at 15:47
• I have a question on Part 3. The instructions say to use 'the second part of this answer' and place it blank 3. Does second part refer to the decrypted value of the second number (315) or the decrypted value of the second set of numbers (245 335 310)? Jul 16 '15 at 17:04