Weekly Challenges: Teach the Teacher

Current Set

Download the latest problem set and challenge yourself—start wherever you are and see how far your reasoning can take you.

Once you’ve worked through a solution you feel confident in, I invite you to teach the teacher: present your thinking as clearly and convincingly as you can.

I have my own solutions prepared, and although we may arrive at them by different paths, the real goal is to compare ideas, refine our understanding, and appreciate the many ways a problem can be seen and solved.

    Past Sets

    Enter the archive as you would a labyrinth—there is no single path, only a series of choices. Each problem set is a doorway, each question a turn that may lead you deeper into unfamiliar territory or back toward ideas you thought you understood.


    Some paths will resist you; others will open unexpectedly. A few may leave you wondering how you arrived there at all.


    There is no map. Choose an entry point, trust your reasoning, and see where the mathematics leads.

    1. Download Challenge Set #01; Download Answer key
    2. Download Challenge Set #02; Download Answer key
    3. Download Challenge Set #03; Download Answer key
    4. Download Challenge Set #04; Download Answer key
    5. Download Challenge Set #05; Download Answer key
    6. Download Challenge Set #06; Download Answer key
    7. Download Challenge Set #07; Download Answer key
    8. Download Challenge Set #08; Download Answer key
    9. Download Challenge Set #09; Download Answer key
    10. Download Challenge Set #10; Download Answer key
    11. Download Challenge Set #11; Download Answer key
    12. Download Challenge Set #12; Download Answer key
    13. Download Challenge Set #13; Download Answer key
    14. Download Challenge Set #14; Download Answer key
    15. Download Challenge Set #15; Download Answer key
    16. Download Challenge Set #16; Download Answer key
    17. Download Challenge Set #17; Download Answer key
    18. Download Challenge Set #18; Download Answer key
    19. Download Challenge Set #19; Download Answer key
    20. Download Challenge Set #20; Download Answer key
    21. Download Challenge Set #21; Download Answer key
    22. Download Challenge Set #22; Download Answer key
    23. Download Challenge Set #23; Download Answer key
    24. Download Challenge Set #24; Download Answer key
    25. Download Challenge Set #25; Download Answer key
    26. Download Challenge Set #26; Download Answer key
    27. Download Challenge Set #27; Download Answer key
    28. Download Challenge Set #28; Download Answer key
    29. Download Challenge Set #29; Download Answer key
    30. Download Challenge Set #30; Download Answer key
    31. Download Challenge Set #31; Download Answer key
    32. Download Challenge Set #32; Download Answer key
    33. Download Challenge Set #33; Download Answer key
    34. Download Challenge Set #34; Download Answer key
    35. Download Challenge Set #35; Download Answer key
    36. Download Challenge Set #36; Download Answer key
    37. Download Challenge Set #37; Download Answer key
    38. Download Challenge Set #38; Download Answer key
    39. Download Challenge Set #39; Download Answer key
    40. Download Challenge Set #40; Download Answer key
    41. Download Challenge Set #41; Download Answer key
    42. Download Challenge Set #42; Download Answer key
    43. Download Challenge Set #43; Download Answer key
    44. Download Challenge Set #44; Download Answer key
    45. Download Challenge Set #45; Download Answer key
    46. Download Challenge Set #46; Download Answer key
    47. Download Challenge Set #47; Download Answer key
    48. Download Challenge Set #48; Download Answer key
    49. Download Challenge Set #49; Download Answer key

    Teach the Teacher

    “If you want to learn something, teach it” is often attributed to Richard Feynman, the Nobel Prize–winning physicist known for making difficult ideas accessible. While the phrase captures his spirit, the idea itself is much older. The Roman philosopher Seneca wrote docendo discimus—“by teaching, we learn”—and similar sentiments appear throughout the history of education.


    The principle is simple yet profound: understanding deepens when we are required to explain. Teaching forces us to organize our thoughts, reveal gaps in our reasoning, and confront the limits of what we truly know. It transforms learning from a passive activity into an active one. When you teach, you are not merely recalling information—you are reshaping it, testing it, and making it your own.


    This process is not limited to classrooms. Teaching is a fundamentally human act. Each of us, through conversation and collaboration, explains, questions, and refines ideas. In this sense, we are all teachers. Mathematics, perhaps more than any other discipline, makes this especially visible. To communicate a solution is to construct a logical narrative—to guide another mind step by step from uncertainty toward clarity.


    At its core, teaching is communication. It demands precision, structure, and empathy. A good explanation does more than present an answer; it reveals a way of thinking. In doing so, it not only solves the problem at hand but also equips others with tools for approaching new ones.


    There is also a social dimension. When we share ideas, we invite challenge and alternative perspectives. These interactions sharpen understanding and often lead to insights that would not emerge in isolation. Much of mathematical progress, both historical and personal, arises from this exchange.


    The aim of this project is to make that process visible. You are invited not only to solve problems but also to teach the teacher—to present your reasoning clearly enough that it can be examined, questioned, and appreciated. Agreement is not the only goal; clarity, structure, and insight matter just as much. Different approaches are welcome—they are, in fact, the point.


    Teaching creates a ripple effect. One explanation leads to another; one idea sparks the next. Over time, this shared effort builds something larger than any individual solution: a community grounded in curiosity, reasoning, and the pursuit of understanding.


    So take a problem, follow it as far as you can, and when you’re ready, teach it.


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