8 thoughts on “Pascal’s Triangle: Introduction

    • 23x4567y4 is divisible by 44 i.e. 11 and 4.

      To be divisible by 4, last 2 digits must be div by 4. So y can be 0, 2, 4, 6 or 8.

      Now to be divisible by 11, |(the sum of the digits in even places) – (the sum of the digits in odd places)| should be divisible by 11 (or should be 0)

      Sum in odd places is 18 + x and in odd is 13 + y, trying out the various values of y we find that when y = 0, x = 6 to satisfy the condition, similarly
      when y = 2 x = 8,
      when y = 4, no value of x exists
      when y = 6, x = 1 and
      when y = 8, x = 3.

      So minimum x is 1 I guess.


    • If you know the logic, you can generate it in 20-30 seconds anyway. And if you use it a lot then chances are the first 5-6 lines at least may stay in your memory without consciously trying to memorise (I know till line 8 though I never actually sat down to mug it up, just use these numbers so often…)


  1. Yes, I figured it isn’t that difficult if one uses it often. Thanks a lot. 🙂

    I am sure people must have mentioned this to you, but nonetheless hearing it again wouldn’t hurt :p.
    J, what you are doing here via these posts is pretty legendary. You are a blessing. 🙂
    Students like me are indebted to you for life. Thank you very much, again.

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