MathDB

Nelson challenges Telma for the following game: First Telma takes

2^9

numbers from the set

\left\{0,1,2,3,\cdots,1024\right\}

, then Nelson takes

2^8

of the remaining numbers. Then Telma takes

2^7

numbers and successively, until only two numbers remain. Nelson will have to give Telma the difference between these two numbers in euros. What is the largest amount Telma can win, whatever Nelson's strategy is?

Problem Statement