1 to 100 no.s, u pick any 10 element subset of them, can we take any two disjoint subsets of this whose sum is equal?

two dices 1,2,..6. u can assign prob for each face as u want. is there a way to assign prob, so that the sum of face of two dices after rolling has uniform prob over {2,3,..,12}

3. u have alice bob throwing darts on a board of size 1. both are unskilled and through uniformly randomnly on the board. game ends when a prev throw radius < your current throw what is prob that alice winds