Patern in a sequence of numbers

Azazel

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Joined
Jul 16, 2018
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3
Hello guys!
I was playing a game of puzzles and stumbled upon this.
I got really annoyed because I could not understand the tips on how to solve it.

This is the sequence:


And this is the tip on how to solve it:
 
The first digit in each row follows the sequence 1,2,3,... The last is 0. The rest follow the explanation in the hint.
 
… I was playing a game of puzzles and stumbled upon this.
I got really annoyed because I could not understand the tips on how to solve it.
Do you understand that this riddle is not solved only with math? It's a linguistics riddle, too (at least in part).

There are many different "math" solutions (they come from viewing the given list as a sequence of numbers generated entirely by mathematical operations). I'll show an example of two strictly-mathematical solutions, using a shorter riddle, in my next post. Because many solutions are available by mathematics alone, experienced folks know right away that this riddle requires something more than just math, to obtain the game's specific solution. The hint's example is meant to provide only a starting point, to get you thinking about patterns other than arithmetic.

You noted that the hint doesn't help you to solve the riddle. Are you saying that you don't understand the pattern described in the hint's example? Or, are you saying that you recognize a pattern but don't understand how to apply it to the riddle?

In case it's the latter, I'll say the solution uses the hint's pattern to form only one part of each number in the riddle. The remaining parts of each number come from different patterns (each of which IS a strictly-mathematical sequence). Looking at the numbers given in the riddle, do you notice anything about the first digits? The last digits? If you do, then consider filling in the middle part of each number using the pattern shown in the hint.

If you don't recognize any pattern in the hint's example, let us know.

By the way, the hint appears to contain a typo. It seems like line 6:

"one one and one two is 1211"

ought to say:

"one two and one one is 1211"

Agree? :cool:
 
Last edited:
Ugh. The system logged me off, without warning, so I lost some typing. I can't seem to recover it.

I just wanted to show one example of why the riddle cannot be solved solely with math operations (it's because there would be no unique solution, without being provided more information).

Let's say the riddle was shorter. What's the next number: 110, 2110, 3210, 412110, ?

I could create formulas for many different number sequences that begin with those four numbers, but differ beginning with the fifth number.

Here's one formula, showing the fifth number to be y = 1637510

y = (204350/3)⋅x^3 - 409150⋅x^2 + (2257900/3)⋅x - 411490

where x=1 gives the first number, x=2 gives the second number, etc.

Now, I don't particularily like 1637510 as a solution; I'd rather the solution be increased by 2. There's a formula for that, too.

y = (1/12)⋅x^4 + (408695/6)⋅x^3 - (4909765/12)⋅x^2 + (4515775/6)⋅x - 411488

where x=5 gives 1637512

Hence, my example riddle has no unique answer because I didn't specify enough information to narrow the possibilities down to a single result.

Likewise, your riddle needs more than arithmetic. :cool:
 
Thx for the time to reply!
One of my doubts was exactly that line.
"one one and one two is 1211"

I couldnt accept it.
I had never considered that it could be written wrong :p

I tried many number, even random ones and never got the correct answer.

And to your questions, I did recognized the patern, Or at least thought I had.
Seems I was right, but still was getting the answer wrong, so I very likely failed to apply it.

Also it was in the middle of a game, and there were others involved. Eventually people just cheated their way out of it and moved on.

But this really triggered me, so I came here to learn how to solve it :)
 
… this really triggered me …
That's why they are called "riddles", ha

Puzzle makers love to use numbers in ways that mislead people into thinking the pattern comes from some formula.

Like this pattern:

123
123
125
12345
127
1234567
129
123456789

Cheers!
 
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