Find the next two terms in this sequence:
10, 11, 12, 13, 14, 15, 16, 17, 21, 23, 30, 33, ?, ?
Solution
120 and 1,111.
Each term of the sequence is the number 15 written in a different base. 10 is 15 in base 15, 11 is 15 in base 14, etc.
The next two terms are 15 written in base 3 and base 2, which are 120 and 1,111, respectively.
It’s a very devious puzzle and quite the brilliant illustration of how a pattern of thought can lead you astray in solving a problem. This has implications in how we approach more serious problems, not just a brain teaser like this one. It really makes you think how many ills of the world could be avoided if we thought about things from more angles than we do. In that respect, I think, this puzzle has great educational value.