[ANN][iQ CONTEST] 100K iQCash mined! Celebration puzzle: 100 $Waves to winner.

[iQCash]

Contest details:
Total Prizes: 100 Waves.

The contest involves one main puzzle and 2 bonus challenges relating to the following graph:

https://iqcash.net/wp-content/uploads/2018/02/Feb2018ContestSmall.png

The graph comprises arrows which indicate possible paths from Alpha to Beta (of which there are many.)

The main puzzle (Prize 60 Waves):
Given that YELLOW arrows allow travel at twice the speed of BLUE arrows, what are the odds (or what is the probability) that a randomly chosen path will be the fastest possible path from Alpha to Beta? UPDATE: This has been solved below

Bonus question 1 (Prize 20 Waves):
There are two additional iQ Puzzles embedded within the graph. The answer to both of the additional puzzles is the letter 'X'. What are those two puzzles?
UPDATE: This has been half solved on Page 2
UPDATE 2: The other half of this has been half solved on Page 4

Bonus question 2 (Prize 20 Waves):
In order to solve the main puzzle (i.e. this is a hint) you will need to calculate how many paths are possible from Alpha to Beta. This can be done by computer algorithm, a hand-calculation technique (i.e. you don't need to be a programmer to solve any part of this puzzle), or by mathematical formula.
The bonus question 2 prize will be awarded to the best mathematical formula that describes (in proper mathematical language/notation) how many paths are possible from Alpha to Beta.
UPDATE 2: No challenge to our best mathematical formula has been offered yet, so the current solution is looking good to win the 20 Waves for this prize.

UPDATE 3: Contest complete. Total prizes of 105 $Waves awarded to winners.

Provide your answer in a reply to this thread.
The contest will run for two weeks. At that end of that period, if still unsolved, the solution to the puzzle will be revealed and no further prizes will be awarded.
Significant contributions to a puzzle question that lead to the solution will be rewarded with a percentage of the prize for that question.
Winners will need to provide their Waves address to which payment of the prize will be made.

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[iQCash]

Link to the inaugural contest from last year for your interest:
https://bitcointalk.org/index.php?topic=2346692

[slayz0r_]

Bonus question 1

Answer:

Q1 What letter is formed by the yellow arrows at an intersection? ->  "X"
Q2 How many "X" are formed by yellow arrows at intersections? -> "X" (X is 10 in romanian, beacause there are ten "X", see picture)

picture:
https://www.dropbox.com/s/dqszotyihy79p0a/2.png?dl=0

[iQCash]

Bonus question 1

Answer:

Q1 What letter is formed by the yellow arrows at an intersection? ->  "X"
Q2 How many "X" are formed by yellow arrows at intersections? -> "X" (X is 10 in romanian, beacause there are ten "X", see picture)

picture:
https://www.dropbox.com/s/dqszotyihy79p0a/2.png?dl=0

Ha. Nice try, but no, that's neither of the puzzles required.
But the best answer offered within the two weeks, if no fully correct answer is given, will get a consolation prize.

[synthet]

Is it 2^16/2^27 to the first question? ~ 0.05% 

[iQCash]

Is it 2^16/2^27 to the first question? ~ 0.05% 

I'm afraid not.

[Vlad_R]

I think answer should be (2^18)/(2^32)

The answer 0.0061%?   

[iQCash]

I think answer should be (2^18)/(2^32)

The answer 0.0061%?   

Sorry, no.

[Vlad_R]

Got it!
Answer is 120/435 = 27.59%

[Vlad_R]

O! Фaк! Блин

Right answer is 120/415 = 28.92% 

[temmuz]

interesting. Let's try to solve 

[slayz0r_]

bonus question 2:

415 paths are possbile

[slayz0r_]

Main Question:

120/415 = 0.289 -> 28.9 %

[JeremyB]

Bonus question 1:
- Maximum of yellow arrows that could be used in the Q zone is 10 => X in roman numeral.

[toxicpyjamas]

The chance a random path is the fastest path is 31/64 or 48,4375%

[JeremyB]

Bonus question 1:
- Maximum of yellow arrows that could be used in the Q zone is 10 => X in roman numeral.

Variant: optimized path is 10 blue arrows + 10 yellow arrows = X + X

[iQCash]

O! Фaк! Блин

Right answer is 120/415 = 28.92% 

This answer is correct for the main puzzle!
Please describe your method.

[iQCash]

Main Question:

120/415 = 0.289 -> 28.9 %

Correct, but Vlad_r beat you to it. What method did you use?

[iQCash]

O! Фaк! Блин

Right answer is 120/415 = 28.92% 

This answer is correct for the main puzzle!
Please describe your method.

And send me your Waves address.

[iQCash]

There is no correct answer for the bonus questions yet. The prize for these will double if they are not solved in the first week.