2016 AMC 12 A Reflection Notes from H

2016 AMC 12A Log

✅ Correct

Problems 1 → 23

❌ Wrong

Problems 24, 25

• Problem 24: Had the right idea but didn’t continue far enough.
• Problem 25: Didn’t understand the problem even after a video.

📘 Embedded Problems

Problem 24 (paraphrase)

There is a smallest positive real number a such that one can choose a positive real b making all roots of the cubic \(x^3 - a x^2 + b x - a\) real. For this minimal a, the corresponding b is unique. What is that value of b?

AoPS #24 (official)    AoPS video #24    Extra discussion

Problem 25 (paraphrase)

Let k be a positive integer. Bernardo writes perfect squares starting with the smallest having k + 1 digits; after each square, Silvia erases the last k digits of it. They continue until the final two numbers left on the board differ by at least 2. Let f(k) be the smallest positive integer that never appears on the board. Find the sum of the digits of \(f(2)+f(4)+f(6)+\cdots+f(2016)\).

Note from Mrs. Lin :  To understand this question more in details, try 

this video, starting at 24: 11. 

AoPS #25 (official)   AoPS video #25 

2017 AMC 12 B Reflection Notes from H

2017 AMC 12B — Practice Log

Quick reflections and timing notes.

Q1–Q23: all correct ✅ Q22: time sink ⏳ Q24–Q25: not answered ❌

Notable Questions

• #13: Took me a while; need to keep practicing Burnside's lemma/technique. (note to self: revisit topic & drill)
• #22: Became a time sink. Pause sooner; sketch structure, estimate difficulty, and decide quickly whether to skip.
• #24: Didn’t understand the question—unclear how to set up the average. Re-read carefully; translate wording to variables first.
• #25: Ran out of time.

Process & Timing Notes

• Not enough time at the end—was able to draw the diagram but didn’t complete the setup.
• For average/setup questions: define variables immediately, write the equation before computing.
• When a problem starts ballooning (>3–4 minutes without structure), mark and move.

Follow-Up Plan