Question 4
Dinko placed some marbles into one hundred black bags, which are numbered from 1 to 100. Each time, you are allowed to ask Dinko about the parity of the total number of all the marbles in any 15 distinct bags and Dinko will give you the correct answer. What is the least number of times you need to ask Dinko, in order to determine the parity of the number of the marbles in bag 1 correctly? Show an example and prove your answer.
Paper instruction: Give a full solution, subject to the example-or-proof instructions in the question.
Paper instruction: Give a full solution, subject to the example-or-proof instructions in the question.