School-Safe Puzzle Games

Number Progression

Zenith let me know of this excellent challenge.  Looks like it should be easy, but it’s not:

What’s the next sequence in this set?






you may submit your answers below in the comment section; will unmask in several days, thanks.

22 Comments to “Number Progression”

  1. Margot | Profile


    Each line ‘spells out’ the numbers in the row before. In this case, there are three ‘ones’, then two ‘twos’, and one ‘one’. The next line, describing this one, would go as follows: One ‘three’, one ‘one’, two ‘twos’, two ‘ones’. Or


  2. kaminaayato | Profile


  3. falwan | Profile

    I have seen this one before and do not want to burn it.

    nice on though…

  4. Mashplum | PUZZLE MASTER | Profile


  5. madfox | Profile

    how about this: 312211

  6. RaLDoZ | Profile

    the first one can be written as “one 1 or one one”

    which is the second one –> 11 (one one)

    now the second one can be written as” two ones”

    which is the third one –> 21

    now the third one can be written as “one two and one one”

    which if the fourth one –> 1211

    now this can similaryl be written as “one one and one two and two ones”

    5th one —> 111221

    so the 6th one will be –> “three ones two twos and one one”

    –> 312211

    am i right?

  7. suineg | PUZZLE MASTER | Profile

    wow, this seems pretty hard, I will try:
    1–> 11; 11–> 21; 21–> 1211; 1211–> 111221; 111221—>?
    I dont know if I am right but I think you use the values more recent form the past so 1 = 11; if 21 =1211 and 1= 11 then 2= 12 but 21= 1211; the problem its the order do I take 21 or 2 and 1; 12 or 1 and 2 jaja thats hard I will try to explain with this example 1211 can have this result values folowing the previous rules:
    can be 1&2&1&1–> 11&12&11&11= 11121111
    or 1&21&1=–> 11&1211&11= 11121111 same as previous right
    but also can be: 1&2&11=11&12&21=111221, this is the last number known from the sequence, so i guess if 11= 21 12 = 1112 right that fits right I think; so my guess with this numeric sequence is: 11&12&21 (more recent values)
    11=21; 12=1112; 21=1211 so my guess for the next number in the sequence is: “2111121211” I am not sure I am right but it´s my best approach.

  8. Shawn | PUZZLE GRANDMASTER | Profile


    I’ve seen this one before. You have to convert the numbers to word-descriptors, then back into numbers again, with each new number describing the last.

    111221 is “three ones, two twos, and one one”. Convert each word into a number and you get 3 (three) 1 (ones), 2 (two) 2 (twos), and 1 (one) 1 (one).

  9. nimrod | Profile

    man, i haven’t been in here since before we had to login to comment..great site.

  10. Bobo The Bear | PUZZLE MASTER | Profile

    The next entry in the list is 312211.

    Each entry in the list shows the numbers used to verbally describe the previous entry. For example, the fourth entry is 1211, which can be described as having, in order,

    one “one”, one “two”, & two “ones”

    which is: 1 “1”, 1 “2”, & 2 “1’s”

    which is: 111221, the next entry.

    Since the last entry has three “ones”, two “twos”, & one “one”, the next entry is 312211.

  11. suineg | PUZZLE MASTER | Profile

    RK I am still not convinced with my answer because of the relationship between 1–>11 2–> 21; the seed with my answer its not absolute, can have variable values and there is no rules to apply the order so I know it must be wrong, my guess is that is a conceptual and recursive, like a description, still looking…

  12. suineg | PUZZLE MASTER | Profile

    another approach(alternative) … let me see: 1 you have (one) 1 so 1(1)->11
    11 you have (two)1 so 2(1)-> 21
    21 you have(one)2 and (one) 1 –> 1211
    1211 you have (one)1 and (one)2 and (two)1-> 111221
    111221–> you have three(1) and (two) 2 and (one) 1—>
    312211 I think, WOW this is crazy, dont understand it yet jajaja cool.

  13. yash_opened | Profile

    this a famous puzzle,you look at the digits and you say them as you see them, like after writing 1, you read it as one one, and thats what you write as your second number, it goes on and on, the answer to this one is
    312211, and the one after this will be 13112221

  14. diegote | Profile

    Next is

  15. fabricio | Profile

    The answer is

  16. abcbcdcdef | Profile

    312211, I must confess that I have seen this puzzle years ago therefore I know the answer. Though when I saw it for the first time, I have no idea what the relation between the numbers was.

  17. RK | Founder | Profile

    several good explanations above, the answer is 312211

  18. RK | Founder | Profile

    thanks Nimrod, nice to see you back :)

  19. yugesh.karnati | Profile


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