# Can you find the value of the question mark$\color{red}?$

Puzzle:

Find the value of the question mark $\color{red}?$.

$$(2, 13, 47)$$ $$(5, 7, 19)$$ $$(8, 1, \color{red}?)$$

Hint 1: $\color{red}?$ is a prime.

Hint 2: $\color{red}?$ is a cyclops.

Hint 3: $\color{red}?$ is a chain of rings. The middle one is black.

Hint 4: $\color{red}?$ is a twin.

Hint 5: The words dialogue, education, housemaid. What do they all have in common?

I will not accept guessed answers.

Enjoy! :P

Edit: The value has been found, as described in the answer below, but the pattern (or main puzzle, as the answer below has referred it to as) has not been solved just yet. Any thoughts? :)

Ok, nobody found the pattern of my puzzle and explained why $\color{red}? = 5$ and thus I will reveal to you the pattern. $\downarrow\downarrow\downarrow$

\begin{align} 2(4+2) + 13^3 &= 47^2 \\ 2(4+5) + 7^3 &= 19^2 \\ 2(4+8)+1^3 &= \color{red}5^2.\end{align}

I could have done something like

$6(0+2)$, $6(1+2)$ and $6(2+2)$ because now we can replace $\{2, 5, 8\}$ with $\{0,1,2\}$, but I figured the former set would make the puzzle slightly harder :)

I hope you enjoyed! :D

• Congrats on your first puzzle! – NL628 Mar 24 '18 at 7:20
• "there may be many different answers" is a big red flag -- the validity of answers on Puzzling should not be based on opinion, that is, someone should be able to tell what the correct answer is from the question alone. I would try to amend the question to limit it to a single answer before this gets closed as too broad. – ffao Mar 24 '18 at 7:27
• @ffao I agree. But, I feel that putting "The answer is NOT -9" is probably enough to make it not broad XD – NL628 Mar 24 '18 at 7:28
• @ffao ok. Thank you for telling me. I was not aware of that. – user477343 Mar 24 '18 at 7:28
• If many answers could fit, then the puzzle is under-specified. A well-crafted puzzle will give enough information to rule in the intended solution while ruling out everything else. Also, keep in mind that (at least here) puzzles are not interactive challenges—potential solutions should be testable by referring to the puzzle, not by needing a response from the setter as to whether they're right or not. If the puzzle lacks enough specificity to make that determination, then it's probably too broad, and any "hints" added to fix that aren't really hints, they're a necessary part of the puzzle. – Rubio Mar 24 '18 at 7:29

Is it

5?

Hint #1:

Five is prime.

Hint #2:

Five is the decimal representation of binary cyclops number 101 (http://oeis.org/wiki/Cyclops_numbers)

Hint #3:

The 5 Olympic rings, blue, yellow, black, green and red.

Hint #4:

5 is a twin number (primes differing by two) with $(3, 5)$ and $(5, 7)$.

Hint #5:

They share the five Latin characters representing vowel sounds .

From a comment:

"There are many different answers": Leaving out some hints, yes, there might be some ridiculously high number also fitting.

The main puzzle:

Hmm. For the first two columns, we see $x_{2,a} = (x_{1,a}*3) - (x_{0,a}-x_{1,a})$ (where $x_{n,m}$ is rom $m$ column $n$), however that for the third row gives $x_{2,2} = 9$.

Old:

Row one; $(2, 13, 47)$: Prime number $15$ ($13 + 2$) is $47$. It is also the second non-consecutive supersingular prime and the 13th supersingular prime overall.
Row two; $(5, 7, 19)$: $19$ is the 8th prime number and it's the seventh Mersenne prime exponent. Row three; $(8, 1, ?)$: $5$ is the first safe prime, Wilson prime, good prime and more.

EDIT:
Main puzzle:

Main puzzle answer is incorrect. Hmm. I see that the first two rows are all prime: $(2,13,47) (5,7,19)$, but $8$ and $1$ aren't.

• I think you have it apart from the main puzzle. – Willtech Mar 24 '18 at 11:34
• You have the right answer, good job! But the pattern is not correct. In two more days, if nobody has given the pattern, I will mark this answer as accepted and explain to you the pattern :) – user477343 Mar 24 '18 at 11:46
• @Willtech Oops. Think I've been puzzling too long. – Duncan Whyte Mar 25 '18 at 9:48

Is it

-9?

Because

The first column is in arithmetic sequence and so is the second so I'm assuming the third is too?

Close? Not Close? Too far away? :P

• Close :) I wanted people to think that, hahah. Good try though $(+1)$ ...... Oh crap, I have reached my daily voting limit. I have to wait $16$ hours before I can vote again. – user477343 Mar 24 '18 at 7:25
• Haha Lol Don't worry about it :P – NL628 Mar 24 '18 at 7:27
• You have the right idea at least :)) – user477343 Mar 24 '18 at 7:27

I am expecting the answer will be

3 or 17

based on hint 4

• But based on Hint $4$, it could be $9857$, right? Both the suggestions are incorrect. – user477343 Mar 24 '18 at 9:29
• But I think a twin prime numbers is a series of a prime number which has the difference of 2 so I came up with these two guess need hints more specific. so it can not be 4 8 5 7 – CodeLover1540 Mar 24 '18 at 9:39
• $9857$ is a twin prime. If you $+2$, we have $9859$ which is also prime. I am not accepting guesses. – user477343 Mar 24 '18 at 11:57
• $5$ is a twin prime with both $(3, 5)$ and $(5, 7)$. $7$ is a twin prime with $(5, 7)$. $4$ and $8$ are not primes; thus they're never twin primes. – Duncan Whyte Mar 25 '18 at 9:05
• Yes, and what is your point exactly? I knew this. The only thing I can say is that sometimes a twin prime is referred to as a prime number such that if you $+2$, it is also prime. Take the following site for instance: primes.utm.edu/lists/small/100ktwins.txt. But sometimes, twin primes are defined as by what you said, how if you $\pm 2$ from a prime, it is also prime. What I am saying, though, is that no matter how we both interpret a twin prime, Hint $4$ still implies that $\color{red}?$ does not have to be $3$ or $17$, but infinitely many other values. – user477343 Mar 25 '18 at 9:13