Math Question

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Chichén Itzá was a Mayan city in what is now Mexico. The picture below shows El Castillo, also known as the pyramid of Kukulcán, which is a pyramid located in the ruins of Chichén Itzá.

The temple at the top of the pyramid is approximately 24 meters above the ground, and there are 91 steps leading up to the temple. How high above the ground would you be if you were standing on the 50th step?

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12 thoughts on “Math Question

  1. Beyond the math, I’d include a follow-up question: supposing that those who constructed this temple could have chosen ANY number of steps, why was 91 selected?

    BTW, what GRADE level is this question in the Common Core standard? Guess?

  2. Ratio of 50 steps out of a total of 90 steps: 50 steps/90 steps
    Ratio of 50/90 out of total height of 24 meters: 50/90 X 24 meters
    Ratio of .56 of total 24 meters: .56 X 24 meters = 13.33 meters

    No higher than 9th grade guessed by my high school math teacher spouse. But we’re old and are only have experience in the public school systems of Ohio and Michigan during years past. I would expect a private school today to teach this much earlier; definitely elementary school. I remember being a freshman at Miami and all the kids who came from Cleveland parochial schools being so much further advanced than me, even though I scored a perfect on the entrance exam.

    1. Just for the record, I recognized the number “91” so all I had to do was check to make sure I was correct. I’ve always had this uncanny recognition of the relationship between numbers. For example, on tests with multiple choice answers, I could narrow it down to a definite two by using pure math. Then I could check the position relationship of the remaining two choices (i.e. C. or D.) to the pattern of the correct answers preceding and following on the test score sheet (it even works when answers are randomly generated). Even when I should have gotten only a 97% based on only knowledge, I got a 100% by guessing on the position of the correct answer when unsure.

      On this one I had one of the “common*” variables (the temple) switched with another common variable (the ground), but because they were both the same value my answer was the same. The variables were “common” because they related to the 91 steps in an identical way.

      Here’s how I correctly guessed the 91 steps:
      1. 91 is near 90-degrees, a right angle or 1/4 of a circle
      2. 4 90-degree angles make a complete square or a complete circle
      3. Now I thought about all the sets of numbers containing numbers near 90 that when added together make a complete set.
      (Examples of sets: 12 dozen make a gross, 4 six packs make a case, 10 dimes make a dollar, two shoes make a pair, 4 seasons make a year, etc.)
      4. Then I crosschecked that list against things I know about ancient temples

      And that’s how I made a good living in the latter part of the 20th Century (computers became widespread, especially in finance, and they just basically compare sets of numbers).
      *

  3. Wow! You are aggressive in your attack of this problem! I like your thinking and reasoning. Your math re the steps is A+. By the way, this is a 6 th grade example problem.

    Did you finalize the “91” steps question?

    1. Yes, but I didn’t want to deprive other readers by giving the answer. I pretty much gave all the hints to the solution, but here’s another one.

      There are on average 91.25 days in every quarter (not by our calendar months) of the year (4 seasons), based on a year of 365 days. That’s where I recognized the number “91”. The hard part was trying to figure out a variable that made 4 X .25 = 1 (the common variable) make sense.

      And then where does Leap Year figure in or even the 1,000 year rule of adjustment. I’m just guessing, and maybe you know, did they make the adjustment for Leap Year by adjusting the height of the “common” variable? If they observed the sun long enough to figure out the 91 steps, surely they noticed adding the “common” variable did not completely solve the problem. (I just realized if that they may have adjusted the height of each step to remove the need for a fourth year adjustment. Wow, that would be impressive and indicate they kept long records.)

  4. Nailed it, as I thought! I wonder how many 6 th graders would observe that the structure is a square pyramid with 4 Sides and 4 sets of stairs and compute 4 x 91 = 364? Then a bell rings!b

  5. I asked that question to M_R a few posts back, and he doesn’t even give “one-liners as ‘comments’….touche, my friend, lol….

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