What is the next number in his series 32 16 19 20 10 13 14?

Answer 1

7

Answer 2

Any number that you choose can be the next number. It is easy to find a rule based on a polynomial of order 7 such that the first seven numbers are as listed in the question followed by the chosen next number. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
For example, the rule:U(n) = (-31*n^6 + 693*n^5 - 5935*n^4 + 24315*n^3 - 48274*n^2 + 40272*n - 3360)/240 generates the above numbers for for n = 1, 2, 3, ... , 7 and n = 8 gives the next number as 206.
On what basis can this rule be described, in any way, as less correct than any other rule?

Answer 3

7. Your pattern is divide by 2, add 3, add 1.

Answer 4

7