"I Know All the USACO Topics! Why Haven't I Qualified for Silver Yet?"

I receive this question from students constantly. They've been coding since they were super young; implement questions perfectly well in class; and can explain anything from complementary counting to inverse indexing with ease. This is an incredibly impressive skill level, especially considering that these kids are hardly even teenagers (and sometimes younger)! By this level, students are generally capable of implementing basic software engineering code with the ease of a professional. So why are they scoring so far below the cut-off?

For many academic competitions, USACO very much included, the actual syllabus of topics sounds trivial, yet the questions themselves are very challenging. However, knowing each topic is far from adequate when it comes to being able to solve the questions; you need to practice using the toolset of topics you know in order to solve a larger question.

Consider the following example: one of the easiest question of the past year's contest cycle was Astral Superposition. If your child cannot (1) explain the sample test case by hand and (2) read in and accurately store the inputs, your child does not know the full syllabus of topics yet, and this post does not apply to you yet and you should read here first. For those of you who can easily do (1) and (2) but did not get much credit on this question during this past January test, let's talk about the challenges:

1) Chains of stars replacing one another's spots are a weird edge case to both identify and solve by hand.

2) We have to navigate the matrix in a weird pattern in order to determine overlapping star places.

To overcome challenge 1, there is no shortcut to solving many many question types by hand. USACO loves to have questions that involve a lot of pattern-finding by hand. Sometimes, they even give you a question with virtually no coding whatsoever, but a lot of problem solving. The ability and willingness to try an organized set of examples by hand until you spot a pattern is necessary for qualification. The level of problem solving required is not taught in public schools, and it takes extensive practice to get faster at it.

To overcome challenge 2, having solved questions with a matrix before is not enough. You need to be super comfortable navigating around a matrix. As an exercise, try looping over a matrix in every possible ordering imaginable. If you can't do any possible looping order in less than 5 minutes, your speed is not yet ready for Silver qualification. Additionally, practice rotating matrices, navigating around matrices based on set directions, testing for boundary conditions, and stamping smaller matrices inside larger matrices. Looping over a matrix by rows, then columns is a necessary but far from sufficient skill level to solve this question.

Even students who are capable of overcoming each of these challenges spend too long doing so. 30 minutes on this question is a good upper bound in order to have enough remaining time to finish the exam with a qualifying score. That is why practice is essential. The qualifiers aren't naturally more gifted; they have spent thousands more hours thinking before the contest in order to save time on the contest.

Of course, these are far from the only skills needed to qualify for USACO Silver. During private and group lessons, I go through each Bronze topic thoroughly in order to ensure that all my students know exactly what practicing to do in order to qualify. But if you know all the topics -- and can solve the questions fully on your own with unlimited time -- then simply do the following:

1) If you are in middle school, solve at least 70 USACO questions.

2) If you are in high school, solve at least 50 USACO questions.

3) If you have already qualified for AIME, solve at least 25 USACO questions.

If anyone helps you with the USACO question (whether by categorizing the question type for you, or by giving you a tiny hint any step along the way), then the question does not count towards your total. You must solve a ton of questions independently in order to quickly solve questions independently. As you solve questions, keep an organized list that tracks the patterns and techniques you used. This will help you identify patterns.

I recognize that 70 multi-hour questions, some of which you might not have the skills to solve without help, is a daunting task. That's why it's such an achievement to qualify. There is fundamentally not enough time on the test to invent every step of the process from scratch. You must be so familiar with the standard patterns of USACO questions that very few lines of code require thought. Therefore, you get a lot of time during the test to think about a small number of creative lines.