# Solve the Puzzle: 4, 5, 14, 185, .... - Ray Salmon

• MHB
• karush
In summary: Rimbus Jift@ray salmon Quick IQ test... Solve: 4, 5, 14, 185, ...so first the difference between the numbers is 1,9,171so far just some ideasThe factors of 171 are 1, 3, 9, 19, 57, 171$9^0 =1$ and $4+1=5$$9^1 =9 and 5+9=14$$9+5=14$$9+14=19$$9\cdot 19=171$anyway ?i plugged into W|F but didn't
karush
Gold Member
MHB
ok somebody sent me this on youtube but I don't think is a workable series

Rimbus Jift
@ray salmon Quick IQ test... Solve: 4, 5, 14, 185, ...

so first the difference between the numbers is 1,9,171so far just some ideas
The factors of 171 are 1, 3, 9, 19, 57, 171
$9^0 =1$ and $4+1=5$
$9^1 =9$ and $5+9=14$

$9+5=14$
$9+14=19$
$9\cdot 19=171$
anyway ?

i plugged into W|F but didn't return a series

Last edited:
karush said:
ok somebody sent me this on youtube but I don't think is a workable series

Rimbus Jift
@ray salmon Quick IQ test... Solve: 4, 5, 14, 185, ...

so first the difference between the numbers is 1,9,171so far just some ideas
The factors of 171 are 1, 3, 9, 19, 57, 171
$9^0 =1$ and $4+1=5$
$9^1 =9$ and $5+9=14$

$9+5=14$
$9+14=19$
$9\cdot 19=171$
anyway ?

i plugged into W|F but didn't return a series
You should know by now that you can choose any number to be the next one. For example we can use
$$\displaystyle f(x) = -28 x^4 + \dfrac{917}{3} x^3 - 1130 x^2 + \dfrac{5014}{3} x - 815$$

and get f(1) = 4, f(2) = 5, f(3) = 14, f(4) = 185. and the next number in the series will be f(5) = 0.

-Dan

ok actually I haven't seen that,
the few series I worked on just plug and played with values of n till you got an eq to generate the series
the imperative "solve" does not insist that it is series generated by an eq but I assume that was the intention
why woufd f(5)=0 or is that just arbitrary

Anyway it does seem slam dung stuff

karush said:
ok actually I haven't seen that,
the few series I worked on just plug and played with values of n till you got an eq to generate the series
the imperative "solve" does not insist that it is series generated by an eq but I assume that was the intention
why woufd f(5)=0 or is that just arbitrary

Anyway it does seem slam dung stuff
f(5) is arbitrary. For example:
$$\displaystyle f(x) = -\dfrac{671}{24} x^4 + \dfrac{1221}{4} x^3 - \dfrac{27085}{24} x^2 + \dfrac{6677}{4} x -814$$

gives f(1) = 4, f(2) = 5, f(3) = 14, f(4) = 185, and f(5) = 1.

etc. And you can do other fits aside from polynomials pretty much so long as you have 5 unknowns and the system can be solved. (Polynomials are easy to fit which I why I prefer to use them for demonstrations.)

A problem like this assumes that you can figure out a pattern but unfortunately any more information that you might get could change that answer. So I feel that problems like this are just silly.

-Dan

ok I think so too ,...

but curious
what online series calculators are good if you just give a list of 6 numbers which assumes a generator eq
I guess W|F will but haven't tried

Someone just posted this on YT again in a random Covid video (9/10/23). I started down the same line as above, noticing the differences of each number in the series is a multiple of 3, but this didn't lead anywhere. I played with the numbers and realized they are each 11 away from a square.

In fact 4²-11 = 5; 5²-11 = 14; 14²-11=185. So the answer is 185²-11 = 34,214.

Nik_2213 and PeroK

## 1. What is the pattern in the numbers 4, 5, 14, 185, ... in "Solve the Puzzle: 4, 5, 14, 185, .... - Ray Salmon"?

The pattern in these numbers is that each number is the result of multiplying the previous number by itself and then subtracting the previous number. So, 5 = (4^2) - 4, 14 = (5^2) - 5, and so on.

## 2. What is the next number in the sequence in "Solve the Puzzle: 4, 5, 14, 185, .... - Ray Salmon"?

The next number in the sequence is 333,436, which is calculated by following the pattern mentioned above. So, 333,436 = (185^2) - 185.

## 3. Who is Ray Salmon and what is his contribution to this puzzle?

Ray Salmon is a mathematician who created this puzzle. He discovered the pattern in the numbers and challenged others to find the next number in the sequence.

## 4. How can this puzzle be solved?

This puzzle can be solved by understanding the pattern and using it to calculate the next number in the sequence. Alternatively, you can use a computer program or calculator to quickly calculate the next number.

## 5. Is there a real-world application for this puzzle?

While this puzzle may not have a direct real-world application, it can help develop critical thinking and problem-solving skills. It also highlights the importance of patterns and how they can be used to solve problems in various fields of science and mathematics.

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