Hongyi is making a triangular display of widgets. the bottom layer will contain n widgets. the layer immediately above it will contain n − 1 widgets. each subsequent layer will contain one fewer widget than the previous layer, and the top layer will contain one widget. if widgets are packed 25 per case, and hongyi must use all of the widgets in every case he opens, what is the smallest positive number of widgets hongyi can use to build the display?

Achild has a box full of colored building blocks. she will choose one block without looking. the odds against choosing a blue block are 4/7. what is the probability of choosing a blue block? amanda is playing a role-playing game with her friends. she will roll dice to determine if her character unlocks a treasure chest. the probability of her character unlocking the treasure chest is 13/20. find the odds in favor of her character unlocking the treasure chest.