Mental calculation

BogdanovBelsky_UstnySchet.jpg (108 KB)

“the looks on the faces of the students in this 1895 painting by n. bogdanov-belsky are wonderful. i love moments when everyone is really focused on trying to figure something out. they are counting in their heads and feeling hopeful and confident that they can solve the puzzle shown on the board if they just think a little more…

(10^2 + 11^2 + 12^2 + 13^2 + 14^2) / 365

try it – no calculating aids allowed!”
amandabauer.blogspot.com/2010/02/mental-calculation.html

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    29 Responses to Mental calculation

    1. I love this. Amazing find, Atk. I have never heard of this painter before and he’s already in my top 10.

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    2. Took me about two minutes to work it out entirely in my head – no paper, no calculator, no cheating. It’s not really that hard. The only thing “hard” about it is remembering the previous numbers when you go to add them up. Each individual calculation is pretty simple. Most folks had to memorize the times table through to 12 as kids, and 13*13 and 14*14 is easy enough to do in your head. It’s even easier to do in your head as the partial sums of the top turn into a number (trying not to give too much away for those still working on it) that makes remembering the numbers simple.

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    3. Oh how the times have changed. Laziness due to technology. Dumbing down down down.

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    4. I worked it out in my head, but it took me a minute. When I noticed that 13^2 + 14^2 was 365, I added up the first three. So I got 2. Mostly my big hangup was not knowing offhand what 14^2 was so I had to do that, and I kept getting distracted thinking about sex.

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    5. The answer is 2.

      It just takes remembering what numbers are times themselves (or more correctly, to the second power) then adding them up. Sadly, I thought it was going to be something/365, even after realizing the first three number equaled 365. Never memorized 13^2 or 14^2, so I had to do them in my head quickly.

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    6. Took about half a minute in the head.  It’s 2.

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    7. took me more like 5 minutes 🙂
      is there a clever way to do this? i guess the point of the exercise is keeping your mind organized enough to calculate, store, and sort at the same time. today, we learn to use aids to do the first 2. this makes the sorting process less “conscious”, i.e just plugging in the different numbers different places and see if we get something that looks like the kind of answer maths tasks generally have…like…2?
      great post atk

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      • The trick is to add them as you go and then realize that once you’ve gotten halfway through it, you’ve got 365, and then hypothesize that the other half will also equal 365 so you get a nice pat answer like 2 out of that long pile of goop, and then test the hypothesis, be satisfied by the result, and publish. SCIENCE!

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    8. The question should be why mathematics are being taught to dirt poor Russian peasants .

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    9. I liked that a lot, and I really stumbled over the answer more then I really calculated it. I added 10²; 11² and 12² together in my head, since the result was easy enough to remember I started anew with 13² and 14² and noticed the results was the same as for the previous three, so the answer was easy enough…but yah, took me a couple of minutes.

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      • I guesstimated. I figured the answer was a whole number, evenly divisible by 365. Not hard to figure 365*2=730 and 365*3=1095, so I guessed 2. Working w/ 365 is pretty easy since we work w/ 360 for so many daily things.
        Prolly about a minute of think time, tops.

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    10. man fuk math u aint nevr guna use dat shit in rel life yo

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    11. There is of course a simpler way you could do this much more quickly, which I actually use a lot.

      By simple assuming that the answer wouldn’t be anything like 3,7575397 and that it’s very likely that the number is an integer, you can guess your way through this. Everybody knows that 10² (or 10*10) is 100 and most people know that 15*15 is 225, so you can kinda assume that all results will be in the ballpark between 100 and 200, if you roughly estimate the average to be around 150 and simple take that 5 times (for each number from 10 to 14) you end up with 750…so you know after about 10 seconds that the results will unlikely be 1 and also very unlikely be 3. Am I making any sense at all?

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    12. I used Excel, and still got the wrong number.

      It helps if you use =sum(a1:a5) and not =sum(a1,a5). I knew it was wrong, I just couldn’t figure why it was wrong.

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    13. rearrange it as:
      (x-2)^2 + (x-1)^2 + x^2 + (x+1)^2 + (x+2)^2 / 365
      which simplifies to:
      5x^2 + 10 / 365

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