My friend gave me this sequence of numbers:







Which number can replace the question mark?

  • $\begingroup$ This is the original! $\endgroup$ – Tanton Aug 16 '19 at 9:28
  • $\begingroup$ Does A change the answer? $\endgroup$ – Abbas Aug 16 '19 at 9:37
  • $\begingroup$ A It doesn't make any sense $\endgroup$ – Tanton Aug 16 '19 at 10:34
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    $\begingroup$ Could the last two lines have been replaced with 361114=? instead of adding a variable into the mix? $\endgroup$ – Voldemort's Wrath Aug 16 '19 at 13:17

New Solution:

10. A (hexadecimal) = 10

Another possible Solution could be:

1. Since A is the first letter in the alphabet

If it's


then it's too easy.

  • $\begingroup$ A is just a medium for transformation! $\endgroup$ – Tanton Aug 16 '19 at 9:49
  • $\begingroup$ I'm thinking the last one here is the most applicable, and probably the answer to the question. Can you confirm/deny @Tanton? $\endgroup$ – Birjolaxew Aug 16 '19 at 10:41
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    $\begingroup$ @Tanton maybe you should discuss this with your friend before you accept this answer $\endgroup$ – Adam Aug 16 '19 at 11:14
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    $\begingroup$ This answer currently says that "A (hexadecimal) = 11" but in hexadecimal A means 10. No part of it has any actual explanation that I can make any sense of it. @Tanton I really don't think this should be accepted. $\endgroup$ – Gareth McCaughan Aug 16 '19 at 21:23
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    $\begingroup$ I literally cannot understand what you're saying with this answer. Both "new" and "another possible" solutions ignore the entirety of the puzzle save its final entry and focus on the letter, whose specific inclusion may indeed be relevant somehow but certainly shouldn't be the be-all-end-all of the puzzle. This is supposed to be a sequence of numbers; you've discarded the sequence entirely and just proposed a substitution of number for variable. How is this a solution to the sequence? @Tanton how is this possibly a satisfying answer? $\endgroup$ – Rubio Aug 17 '19 at 15:37

I also have a solution



Think of the number to the left of the sequence as octal


3(octal)= 11(binary)
6(octal)= 12(quanternary)
11(octal)= 13(Senary)
14(octal)= 14(octal)


361114(octal)= 123468(decimal)

  • $\begingroup$ My answer is based on the fact that A has no effect. Because A=123468 is substituted into the next formula, I can't continue to convert. $\endgroup$ – sypicky Aug 16 '19 at 14:41
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    $\begingroup$ What determines the bases used on the right-hand sides? $\endgroup$ – Gareth McCaughan Aug 16 '19 at 21:25
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    $\begingroup$ On the right hand side is a series of even numbers, and adds 2.I think it's a rule. $\endgroup$ – sypicky Aug 17 '19 at 0:05

An alternate solution is:



generally, when you have variable names next to each other (e.g. $xy$) that would mean that you are multiplying their values (e.g. $x\times y$).


you would multiply $11\times12\times13\times14=24024$

  • 1
    $\begingroup$ Also a valid theory, It could be your answer is the one OP's friend was looking for! $\endgroup$ – Abbas Aug 16 '19 at 14:15
  • $\begingroup$ How does this account for things like "11=13" in the question? $\endgroup$ – Gareth McCaughan Aug 16 '19 at 21:24
  • $\begingroup$ Maybe I'm just slow today... why did you select those numbers to multiply? $\endgroup$ – maxathousand Aug 16 '19 at 21:33
  • $\begingroup$ I don't think multipliers can be omitted between numbers. One example is 6÷2 (1 + 2). $\endgroup$ – sypicky Aug 17 '19 at 0:18
  • $\begingroup$ @sypicky - That's true, but neither can you say $3=11$... This is assuming the numbers on the left are variables. $\endgroup$ – Voldemort's Wrath Aug 17 '19 at 1:46

Based on the last but one line, A is


  • $\begingroup$ Well if A is this number then why is 3=11 or 6=12 or 11=13? $\endgroup$ – Adam Aug 16 '19 at 18:48
  • $\begingroup$ As, I have just seen Voldermort's 1st comment to the OP and up-voted it. $\endgroup$ – Mea Culpa Nay Aug 17 '19 at 6:34

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