Excel vs. traditional math

Excel makes it a lot easier to brute force problems.

DC1 was doing some Hard Math for Middle School students problems with different bases.

An example of one of these:  (p.14, #8):  Find all the values of A for which the base 63 number A7894321 (base 63) would end with a zero if it were written in base 10.

The first step to approaching this problem is the same for both approaches– you have to go through the first step of mechanics of turning something base 63 into base 10.  That means realizing each place value means 63 instead of 10 and expanding out. So:

1 + 2(63) + 3 (63^2) + 4 (63^3) + 9 (63^4) + 8 (63^5) + 7 (63^6) + A (63^7)

In Excel, what you then do is you take =1 + 2(63) + 3 (63^2) + 4 (63^3) + 9 (63^4) + 8 (63^5) + 7 (63^6) and fill that down 10 rows.  Then you put in another column that is nothing but =  (63^7), then a third column that is 0, 1, 2, … 9.  In the fourth column you type = A1 + B1*C1 (or whatever your top 3 cells are), and fill down.  A final step is to take those responses which are unhelpfully in exponential “E” format and paste them as values and look at each one to see which end in 0.  (Only 6 in case you were wondering.)

To do this by hand, you will do something called “casting out 10s”.  You only care about the last number, so you don’t have to do all the math, just the last part.  So instead of the full equation above:  1 + (2*3) because you only care about the last digit, + 3 * 3* 3 = 7 + 27 but we only care about the last digit, so we cast out the 3 tens and are left with 4 to which we add 4*3*3*3, and so on.  In the end you will end up with: some number + A*3^7 mod 10 = 0, solve for A.

I use Excel a lot in day-to-day life.

Do you?

Posted in Uncategorized. Tags: . 11 Comments »

11 Responses to “Excel vs. traditional math”

  1. Solitary Diner Says:

    I feel like I just read a post in a completely foreign language….and I used to be good at math! (And not just “good at math for a girl”.)

  2. monsterzero Says:

    I don’t have Office at home so I use Google Sheets, but the fill handle is great for figuring out things like compound interest.

    A couple of car salesmen once tried to get me to sign for a loan at 32% interest. The only way I was able to determine the rate was by using Excel.

    • nicoleandmaggie Says:

      Wow, that’s an insane rate. Spreadsheets are definitely easier for me than digging up the compound interest formula, even though I should have it memorized and can re-derive it quickly enough to get through exams that required I know it. Plus there’s something nice about being able to see each compound as it theoretically happens on the sheet rather than just getting the end number.

  3. yetanotherpfblog Says:

    I’ll use Excel for personal finance or planning, but for one-off problems like this I’d either solve by hand or use Python (my preference for Project Euler puzzles).

  4. chacha1 Says:

    I am occasionally asked to do something in Excel and I basically break out in hives every time. No training = severe anxiety. Generally the things I am asked to do are presentations of text, not really spreadsheet material, and can be accomplished adequately (and less stressfully) in Word tables … so I’ve gotten by.

    • nicoleandmaggie Says:

      Someone told me there’s a really excellent online tutorial for Excel called Linda or Lydia or something. I’ll dig it up.

      I teach the basics of excel (fill down, very basic equations) in a relatively short amount of time in my stats class and the kids who don’t know it often gasp audibly at how cool and useful it is (particularly the fill down part). Though it sounds like you use the presentation stuff more frequently which isn’t too bad either– I find it easier to use than Word tables given that I know how to use both. Excel is way less finicky. Though the newest versions of office make it much easier to transfer one over to the other.

  5. Dana Says:

    I love Excel, I find it isn’t necessarily the best way to do things but it is so widely applicable that it almost always CAN be used to solve a problem in so many fields. I teach a lot about using it in analytical chemistry, I can’t imagine the days of lab reports before Excel.

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