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You take one section of a newspaper and pull out one sheet from among them, to find that page 6 and page 25 are printed on the same side of the sheet. From this fact, can you predict what the page numbers are, printed on the center sheet of the same section?

15,16?

                :cheers:                 ! ;D !

It depends on the Vegas odds and how much $ was bet.  

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I don't think Las Vegas has any bowls with 30 blue and 20 red marbles in them.
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But if Vegas did have bowls with 30 blue and 20 red marbles, and John bet $5 he would draw a red one, then what?

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I think this one is usually harder. You really have to think outside the box!
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                        What is the next number in this sequence?   1, 12, 1, 1, 1, ...

Any number you like.

Choose any 6th number, and one can construct a rule which predicts the sequence.

Same with respect to cosmology. You can find any number of sets of equations that match astronomical observations. Or in maths, you can find any number of polynomials (or other functions) interpolating a given finite set of points.

You operate them in periodical mode. Then you have a beep every

0 4 8 12 16 20 ... minutes

as well as every

0 3 6 9 12 15 18  ... minutes

Five minutes for your egg is e.g. from 3 min (second timer) to 8 min (first timer).


The 3 minutes, before you can start cooking, are not lost. You can e.g. roll a cigarette, light it, and contemplate the quantity of useful plants God created.

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Very good, Struthio! You surprised me. Listing the periodical beeps is an interesting development. 
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This kind of puzzle is older than electronic timers. The answers given for use of hourglass sand timers can also work.
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Incidentally, this puzzle could have easily asked for the next 4 numbers in the sequence, but the 6th number is sufficient and unique.
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This is WAY more information than most recipients of this puzzle have had previously.
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It has been reported that the vast majority of people cannot solve it. So don't feel left out if it's too difficult.
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Perhaps you could give just one example of a rule you have successfully constructed and its corresponding 6th number?
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What, for example, would be your "constructed rule" if the chosen 6th number would be 19?

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That's an interesting website, which would seem to be a reasonable basis for your outlook on this topic.
However, there seems to be a problem.
The formula it provides for the "rule" of operation is always the same formula, regardless of the numbers chosen for the series.
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I tried to change the 6th number from 19 to 13, and the site offered 139 as the 7th, giving the same formula.
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I tried changing the 5th number from 1 to 17 (1,12,1,1,17,...) and the site offered 26 as the 6th, giving the same formula.
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I tried changing the 6th number from 26 to 1 (1,12,1,1,17,1,...) and the site gave -173 as the 7th, giving the same formula.
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No matter what numbers I provide, it guesses the wrong number for the next in the series.
But as soon as I correct the wrong number, it provides another wrong number for the subsequent number following.
And in all cases, the same exact formula is provided as the "rule" that determines the next number.
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So it's not working.
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Try putting in 1,12... and asking for the third number. The site says that 23 is the third number. Wrong: it should be 1.
Try putting in 1,12,1,... and ask for the fourth. It says -32 is the fourth. WRONG: it should be 1.
Try putting in 1,12,1,1,... and ask for the fifth. It says 45 is the fifth. WRONG: it should be 1.
Try putting in 1,12,1,1,1,... and ask for the sixth. It says -54 is the sixth. WRONG: it should be the one I asked for in the puzzle.
We already tried 1,12,1,1,1,19,... and for the next, received 175.
We already tried 1,12,1,1,1,13,... and for the next, got 139.
We already tried 1,12,1,1,1,17,... and for the next, got 26.
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And the real kicker is, 

So just for kicks, let me give you the correct 6th number, which is 2. The site has been unable to provide that number.
Now, given the correct series from the puzzle, 1,12,1,1,1,2,... what does the site give as the formula?
That's right. It provides the same formula as it did for 1,12,1,1,1,... followed by 19, 13 and 17, all of which were WRONG.
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What does the site provide now for the 7th number in the series after 1,12,1,1,1,2,...? It says 73, which is WRONG.
This site, as interesting as it is, has been UNABLE to correctly anticipate ANY of the numbers in this series, even the THIRD (1).
And it gives the same formula FOR EVERYTHING, which by all reasonable expectations, must also be WRONG.
This formula has exactly NOTHING to do with the very simple fact which correctly predicts all the numbers in the puzzle series.
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Formula used:

Where, x and y are the coordinates

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The site offers calculation of Lagrange polynomials.
Apparently what this puzzle asks for has nothing to do with Lagrange polynomials.
So their formula doesn't work on this puzzle.
If Lagrange polynomials are for constructing curves, perhaps it would help to know that the puzzle is not based on any curve.

Neil Obstat,

the question I answered was

What, for example, would be your "constructed rule" if the chosen 6th number would be 19?

I presented a rule which can be used to produce the sequence 1,12,1,1,1,19.


Here's another answer, showing that the next number is not the number two:

What is the next number in this sequence?   1, 12, 1, 1, 1, ...

The next number is the number one. The sequence gives the number of cuckoo calls of a cuckoo clock at a quarter to twelve, twelve, a quarter past twelve, half past twelve, a quarter to one, one, etc.