My answer is This is reached by

Based on the other answers the formula for the values is $f(x)=$ (with the first value is for $x=-1$). The question is what is $f(0)$.

And now my computer generated and checked solution: Put the weights in a row and number the places from 1 to 15. Then do the following: I generated these command by an similar algorithm as Murch. ...

Based on Jamal Senjaya answer: Sum is 34 You can create other solutions by using other Fibonacci numbers as start. For example:

4x4 Board You can achieve that in the following way: That solution is optimal because 5x5 Board Solution:

This solution is based on the Jose's answer, but it construct a strategy with an arbitrary win chance. Winning with an arbitrary win chance xnor showed int this post that a group with $2^i-1$ person ...

Here is my solution with the definitly lowest possible number of questions: Question 1 to Alice: Case 1: Alice stays quiet Question 2a to Bob: Case 1.1 Bob stays quiet too: Now we ask the last ...

First you calculate the smallest $n$ with $\frac{1}{2}n(n+1) \geq x$ if $\frac{1}{2}n(n+1)-x$ is odd then increase $n$ by $1$ if $n$ is even or increase $n$ by $2$ if $n$ is odd. Now \$\frac{1}{2}n(n+...