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What number comes next?

Bomb#20 said:
... the best solution is that 6, 12, and 25 are the products of successive integers with successive prime numbers: 3 * 2, 4 * 3, 5 * 5. :wink:

New problem: what number comes next after 6, 13, 25?
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No takers? No worries. That one's an easy quadratic sequence: 6 + 7 = 13, 13 + 12 = 25, 25 + 17 = 42.

Those were warm-up problems; today's the main event. As always, The Answer is 42; the challenge is to discover The Question. Can you find a mathematical formula fn that fits 6, 14, 25 and that makes 42 the answer to "What's the next value of fn?"

ETA: No cubics.
 
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Bomb#20 said:
Swammerdami said:
6 12 25 ?

I'll guess the intended solution is 20. Because 6, 12, 25, 20 give today's date as month, day, year, century. Am I the only one that despises America's reversal of month and day in what would otherwise be a logically ordered sequence? What countries other than USA have acquiesced to this inanity?
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Are you suggesting 12, 6, 25, 20 is a logically ordered anity? You're still mixing endianness, just switching in different places. Logical ordering would at least be 21, 60, 5202. Better would be 1749711600 -- that's SI. :biggrina:

  • 52 (followed by 64) is plausible if this is an ordered list of cardinalities associated with games: There are SIX die faces, TWELVE goal spots in Shut-the-Box (and 12 white checkers pieces, and 12 zodiac signs), 25 slots on a Bingo card (or letters in a certain word game), and 52 cards in a standard deck.
  • Less likely is 51, which matches several possibilities including 1,3,6,12,25,51,103,... -- the floors of the golden geometric sequence with ratio 2: 1.618, 3.236, 6.472, 12.944, 25.888, 51.777.
  • A dark-horse candidate is 85 (see https://oeis.org/A034875 "1, 2, 6, 12, 25, 85, 194, 590, 1695, 4879, 19077, 83994, 167988, 1041780, ... Smallest integer not the sum of powers of some earlier terms."
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Of course there are infinitely many solutions to this sort of problem; but the intent was for a mathematical pattern, ideally one that's convincingly better than alternatives -- it should cry out that it's not just an answer, but The Answer. So good theories, all of you, but the best solution is that 6, 12, and 25 are the products of successive integers with successive prime numbers: 3 * 2, 4 * 3, 5 * 5. :wink:

New problem: what number comes next after 6, 13, 25?
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Harumph!!!! Ahem...couigh..cough

Why is prime numbers the best solution? I guessed it had to do with prime numbers because prime numbers are a perennial topic on the forum and appear in problems. I am only vaguely familiar with prime numbers beyond he basic definition.

Being from electronics powers of 2 jumped out.
 
steve_bank said:
Harumph!!!! Ahem...couigh..cough

Why is prime numbers the best solution?
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Because the next number in that sequence is 42! :biggrina:

(If that doesn't clear things up, quit wasting your time reading IIDB and go read The Hitchhiker's Guide to the Galaxy.)
 
Bomb#20 said:
Swammerdami said:
6 12 25 ?

I'll guess the intended solution is 20. Because 6, 12, 25, 20 give today's date as month, day, year, century. Am I the only one that despises America's reversal of month and day in what would otherwise be a logically ordered sequence? What countries other than USA have acquiesced to this inanity?
Click to expand...
Are you suggesting 12, 6, 25, 20 is a logically ordered anity? You're still mixing endianness, just switching in different places. Logical ordering would at least be 21, 60, 5202. Better would be 1749711600 -- that's SI. :biggrina:
Click to expand...

Anity? At least that's better than Inanity, I guess. 8-)

It was almost exactly 50 years ago that I wrote routines to read and write the Time_of_Day Clock on S370.

The TOD was nominally) a 64-bit counter whose bit 51 toggled once every 1 microsecond; bit 31 toggled every 1.048576 seconds; and bit 0 toggled on May 11, 1971. I had a routine to convert the binary counter to a readable string. Rather than writing tedious code to convert in the opposite direction, I just started with all zeros, and or'ed in 1's MSB to LSB according as how the converted date sorted above or below operator input. This works only because the format (right now "2025/06/14/13:16:24 GMT") is in perfect sortable order.

(The TOD clock "knows" whether it's been Set or not. If not set the operator is asked to set it during IPL, but if already Set (as might happen if diagnostics had been run) the operator would NOT be invited to set it, and the OS might crash if the clock had a very wrong value. That's why I needed to set the clock correctly.)

From the trivia desk: S370 Principles require that the TOD yield different values for successive reads, but the Model 135 updates the clock only once every 16 microseconds. To ensure compliance with The Principles the Read Clock instruction on that model has a delay loop to ensure that at least 16 microseconds are spent.
 
Bomb#20 said:
steve_bank said:
Harumph!!!! Ahem...couigh..cough

Why is prime numbers the best solution?
Click to expand...
Because the next number in that sequence is 42! :biggrina:

(If that doesn't clear things up, quit wasting your time reading IIDB and go read The Hitchhiker's Guide to the Galaxy.)
Click to expand...
^
The only post in this thread that calls up some glimmer of understanding. The rest of it might as well be Mandarin or Sanskrit.
 
A joke I heard from a physicist.

AE is in the audience listening to a presentaion.

The speaker concludes saying 'Therefore this is true'.

AE asks 'But why must it be true?'

Speaker replies' Because it is written',

'Written where?' asks AE.

Pounding his fist on the lecture the speaker exclaims 'Written in my book!'.
 
Learn so0mething new everyday.

en.wikipedia.org

Fundamental theorem of arithmetic - Wikipedia

en.wikipedia.org en.wikipedia.org

In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 is prime or can be represented uniquely as a product of prime numbers, up to the order of the factors.[a][3][4][5] For example,


1200 = 2^4 * 3^1 * 5^2

The theorem says two things about this example: first, that 1200 can be represented as a product of primes, and second, that no matter how this is done, there will always be exactly four 2s, one 3, two 5s, and no other primes in the product.

The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (for example, 12 = 2 ⋅ 6 = 3 ⋅ 4

This theorem is one of the main reasons why 1 is not considered a prime number: if 1 were prime, then factorization into primes would not be unique; for example, 2 = 2 ⋅ 1 = 2 ⋅ 1 ⋅ 1 = …

The theorem generalizes to other algebraic structures that are called unique factorization domains and include principal ideal domains, Euclidean domains, and polynomial rings over a field. However, the theorem does not hold for algebraic integers. This failure of unique factorization is one of the reasons for the difficulty of the proof of Fermat's Last Theorem. The implicit use of unique factorization in rings of algebraic integers is behind the error of many of the numerous false proofs that have been written during the 358 years between Fermat's statement and Wiles's proof.
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Swammerdami said:
The TOD was nominally) a 64-bit counter whose bit 51 toggled once every 1 microsecond; bit 31 toggled every 1.048576 seconds; and bit 0 toggled on May 11, 1971.
Click to expand...
And for reasons unknown IBM numbers the bits backwards from everybody else (bit 0 is the high order bit)....

Was confused mightily about 370 page tables until this was pointed out...
 
jonatha said:
Swammerdami said:
The TOD was nominally) a 64-bit counter whose bit 51 toggled once every 1 microsecond; bit 31 toggled every 1.048576 seconds; and bit 0 toggled on May 11, 1971.
Click to expand...
And for reasons unknown IBM numbers the bits backwards from everybody else (bit 0 is the high order bit)....

Was confused mightily about 370 page tables until this was pointed out...
Click to expand...

Yes. As I posted I wondered how to number the bits, but since it was an IBM feature I went à la IBM.

That's not the only thing IBM did differently from the rest of the world. Their ICs came in a completely different package shape. AFAIK they were the only manufacturer using "trilead" cables (a "poor man's coax"). Their circuit diagrams showed all gates as rectangles compared with the standard curved shapes for ORs and ANDs. Their terminologies were different. It was said that this was deliberate to hinder engineers from defecting to competitors: An engineer who'd trained only at IBM might be uncomfortable relearning or might come across as ignorant in a job interview.
 
2 3 4 8 9 10 512 513 514 _ _ _ _?

What are the next 4 digits?


IQ test kind of question on pattern recognition.
 
steve_bank said:
2 3 4 8 9 10 512 513 514 _ _ _ _?

What are the next 4 digits?


IQ test kind of question on pattern recognition.
Click to expand...
2 ^3 = 8; 2 ^9 = 512. The pattern is that each set of three consecutive numbers starts with 2 to the power of the middle of the previous triplet.
So the next triplet starts with 2 ^513.
Now obviously Bilby found a (simpler?) pattern. I have also figured it out - 2^3 = 8, 8^3 = 512. Next set starts with 512^3.
As you can see there is more than one possible solution.
 
2^3 = 8
8^3 = 512

2,8,512. The other numbers were noise.



110 130 __ 190

What is the missing number?
 
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