This quiz will include a sampling of all of the major topics that we have covered in this chapter: algebra, number theory, logic, and probability. In addition, each problem represents a sample of what can be expected in other courses on Brilliant.
As you move through these challenging problems, look for ways to apply the problem-solving techniques that you have been practicing. In addition, think about how you can prove your conclusions and how to identify when a rule is always, sometimes, or never true.
Each of the six identical coins has one silver side and one gold side:
Using the arrangement above, is it possible to successively flip over pairs of adjacent coins so that all 6 coins are gold side up?
Note that "flip" indicates switching from gold to silver or back again and "pairs of adjacent coins" means only two coins next to each other may be flipped at a time.
For more problems like this, visit the Joy of Problem Solving course.
One bag contains oranges, one bag contains pears, and one bag contains a mix of both:
Unfortunately, all of the bags are labeled with the wrong labels.
You are allowed to look at one piece of fruit from one bag, and then readjust labels.
What is the minimum number of times that you must complete this process to be sure that all bags are correctly labeled?
For more problems like this, visit the Logic course.
Which is more likely?
For more problems like this, visit the Games of Chance course.