A couple weeks ago, I gave my Advanced Geometry class a problem on a problem set (unrelated to geometry):

I loved that many of my kids figured out the answer. It is .

We then had a couple of “do nows” that related to this. So if you had 100!, what is the highest power of 7 that could go into it evenly? What about 11?

[After playing around with this puzzle, it is possible you will see why asking “What is the highest power of 2 that could go into it evenly” or “what is the highest power of 12 that could go into it evenly” are harder questions that 7, 11, or even 10.]

Kids were wondering if there was an efficient way to solve the problem. I said: yes. I won’t tell you what the way is, but I will introduce you to a math notation that might help… (and then I showed them the floor function).

Today a student in my Advanced Geometry class (who had seen the summation symbol and floor function in his middle school (!)) showed me this that he worked out:

Which is *very close to being correct.* It doesn’t work for composite numbers… But it does work if *y* is a prime number (or a power of a prime number). I pointed out to him that his solution wouldn’t work for the original Algebrainiac Attack problem, but it is very close to being correct. I asked him if he could modify his answers to deal with composite numbers… I am excited to see what he comes up with.

My one good thing? I gave my kids a concrete puzzle, and one kid wanted to generalize it! And he is getting very close to the solution!

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*Related*

What age are your advanced geometry class? And what age are your multivariate class?

Geometry is 9th grade (so around age 14). And Multivariable is 12th grade (so around age 17).