10
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What are the next few numbers in each of these integer sequences? Each of them has a clear and justifiable solution.

1, 2, 3, 5, 8, 9, 12, 20, 21, 22, ??, ??, ...

50, 49, 48, 46, 45, 44, 43, 38, ..., 25, 24, 23, ??, ??, ...

11, 12, 20, 30, 80, 90, 10000, ????

... 4, 5, 6, 8, 10, 40, 46, 60, 61, ??, ??, ...

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    $\begingroup$ Hint: Although all of these are number sequences, none of them have anything to do with the actual numerical properties of the numbers themselves whatsoever. $\endgroup$
    – user88
    Apr 6, 2015 at 9:33
  • $\begingroup$ ,..., means that all numbers in the interval are included? $\endgroup$
    – leoll2
    Apr 6, 2015 at 10:44
  • $\begingroup$ No, it means that the numbers in the sequence between 38 and 25 were omitted, and you need to find the numbers that come after 23. $\endgroup$
    – user88
    Apr 6, 2015 at 10:45
  • $\begingroup$ Any hint for the 2nd sequence? $\endgroup$
    – leoll2
    Apr 12, 2015 at 9:14

6 Answers 6

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Partial answer

1)

23,25

Ordinal numbers that aren't made juxtaposing the cardinal and "-th" suffix.
Credit of this answer to Xyuzhg

3)

Googol

Numbers that when written have exactly 6 letters. 10000=myriad.

4)

64, 80

Nonnegative integers that when written out in full in English have no repeated letter.

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    $\begingroup$ Your answer for sequence 4 is correct. $\endgroup$
    – user88
    Apr 6, 2015 at 9:43
  • $\begingroup$ @JoeZ. I added a solution for sequence 3. If wrong i'll delete it $\endgroup$
    – leoll2
    Apr 6, 2015 at 10:29
  • $\begingroup$ The rule is correct, but you haven't given me the next number. $\endgroup$
    – user88
    Apr 6, 2015 at 10:29
  • $\begingroup$ Googol is too big or ok? $\endgroup$
    – leoll2
    Apr 6, 2015 at 10:37
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    $\begingroup$ Googol is the correct answer. Good job. $\endgroup$
    – user88
    Apr 6, 2015 at 10:38
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Sequence 1:

23, 25 (twenty-third, twenty-fifth)

Reason:

Numbers that when written in the chronological ordinal series (first, second, third, etc.) are not the number appended with "th". ("Eighth" is "eight" + "h".)

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  • $\begingroup$ Our solutions for 1 agree everywhere.. but yours is simpler. $\endgroup$ Apr 6, 2015 at 12:22
  • $\begingroup$ Funny - 0 would be accepted by yours, but not mine. I suppose there are linguistic connections to be made here? $\endgroup$
    – Xyuzhg
    Apr 6, 2015 at 12:31
  • $\begingroup$ Well, it's not surprising that 'th' isn't added in bare to a number ending in 't' or 'y'; "two" is 1 of 2 numbers ending in 'o' and by coincidence it becomes "second"; and I guess that the disappearing 'e' makes some sense. Somehow 'dth', 'nth', 'rth', 'xth' are all natural and easy to pronounce. The other number ending in 'o', "zero", happens to not become something special and so gets 'oth', which is also not a problem to speak. $\endgroup$ Apr 6, 2015 at 13:10
  • $\begingroup$ @Xyuzhg: I didn't include zero because I started counting from 1. $\endgroup$
    – user88
    Apr 6, 2015 at 21:05
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The second sequence is:

21, 20

And the pattern is

the number of stars on the US flag in reverse order.

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1) All numbers when written out (googol would be ten duotrigintillion) end in one of these letters: denortxy (sorted alphabetically). Take only the even spots of "denortxy" to get "eoty", and now all numbers ending in a letter from "eoty" are in our list.

..., 23, 25, 28, 29, ...

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  • $\begingroup$ Twenty ends in "y". $\endgroup$
    – user88
    Apr 6, 2015 at 10:34
  • $\begingroup$ Right, aeiouy then. $\endgroup$ Apr 6, 2015 at 10:35
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    $\begingroup$ Also, "eight" ends in "t". $\endgroup$
    – user88
    Apr 6, 2015 at 10:35
  • $\begingroup$ Oh okay nevermind then, I'll think about it. $\endgroup$ Apr 6, 2015 at 10:36
  • $\begingroup$ "Numbers that end in aeiouy when spelled out normally or that can end in e when spelled out how they sound" works for everything.. $\endgroup$ Apr 6, 2015 at 10:38
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Sequence 2:

The sequence repeats its interval at every 25
50, 49, 48, 46, 45, 44, 43, 38
25, 24, 23, 21, 20, 19, 18, 13

my closest guess anyways

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  • $\begingroup$ There are numbers between 23 and 38 in the sequence. $\endgroup$
    – user88
    Jul 14, 2016 at 19:48
0
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sequence 2 29, 34 Pattern -1,-1,-2,-1,-1,-1,-5, then repeats -1,-1,+6,+5

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    $\begingroup$ Please hide your answer in spoiler tags. $\endgroup$ Jul 28, 2020 at 0:52
  • $\begingroup$ how do i do that ? $\endgroup$ Jul 31, 2020 at 1:07
  • $\begingroup$ That's okay, it's one now. $\endgroup$ Jul 31, 2020 at 12:45

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