Q: You have 8 batteries but only 4 of them work and 2 are needed to power a flashlight. What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?
A: 7. If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries.