
Member 11577008 wrote: OK... I failed to do it in my head, but worked it out in text below then checked it in Excel
Upvote for honesty.
Member 11577008 wrote: So... I'm dumber than a 19th century schoolboy
Don't count on it, from what I can see in the picture there is one kid that whispers something in the ear of the teacher, the rest are still thinking.
Wrong is evil and must be defeated.  Jeff Ello
Never stop dreaming  Freddie Kruger





To solve mentally with no use of paper, I need to imagine 5 squares, made of stones laid out on a table.
we have first square that is made of 10x10 red stones.
second square is made of 10x10 red stones plus 1x10 green stones at top and 10x1 green stones at right, then to fill the square we have a 1x1 square of blue stones at top right corner.
third square is made of 10x10 red stones plus 2x10 green stones at top and 10x2 green stones at right, we fill the square with 2x2 stones.
etc...
red stones are 500 (5x10x10)
green stones are 200 (20 on second square, 40 on third, 60 on fourth, 80 on fifth)
blue stones (squares of 1, 2, 3, 4) are 1+4+9+16 = 30
total 730 stones.
730 / 365 = 2.





Visual solving, I like it.
Wrong is evil and must be defeated.  Jeff Ello
Never stop dreaming  Freddie Kruger





The difference of two consecutive squares is the higher number * 2  1. So 11^2 = 10^2 + (11 * 2)  1 = 100 + 22  1 = 121. Therefore the answer is [(100 * 5) + (11*21)*4 + (12*21)*3 + (13*21)*2 + (14*21)] / 365 = 2. My gut answer is that the answer was probably an integer with 2 being likely.





e
looks like the same kind of sequence.





Easiest i could think of was to simplify the numerator to (122)^2+(121)^2+12^2+(12+1)^2+(12+2)^2
And then it becomes a more manageable 5*12^2 + 2*1^2 + 2*2^2
At which point most folks would find it easy to compute the numerator to 730. Some may even factor out the 5.





This is how I mentally solved it. Well, I used my fingers, also.
10^2 + (10 + 1)^2 + ... + (10 + 4)^2
taking into account (a + b)^2 = a^2 + 2ab + b^2, we have
10^2 appears 5 times: 500
the 2ab term gives:
2 * (10*1 + 10*2 + 10*3 + 10*4) = 20 * (1 + 2 + 3 + 4) = 200; 700, up to now
then, the sum of the squares:
1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30.
numerator sums 730. denominator: 350 + 15, times two gives 700 + 30;
answer: 2





Brute force. All in head, no paper or anything else. Wrote the post after doing it.
10x10 = 100
11x10 = 110+11 = 121 (don't remember this one)
12x12 = 144
subtotal = 365
13x10 = 130+39 = 169 (don't remember this one)
14x10 = 140+56 = 196 (don't remember this one)
subtotal = 365
total = 730
divide by 365 = 2
Add one more pair of numbers and I might not have been able to do it. I dropped the 169 on the floor once before adding the second pair.
I never learned the complete multiplication tables as I could do the above sort of math quickly enough to get by.





I arrived at "approx 2" like so:
Jörgen Andersson wrote: 10^{2} + 11^{2} + 12^{2} + 13^{2} + 14^{2}
is approx. 5 * 144 (at least one square I know) Take the five out of 365 And you have 144/73 = 2ish.
"If we don't change direction, we'll end up where we're going"





Five consecutive squares always average to the middle square plus 2.
146 * 5 = 730.
Answer = 2





That is some amazing trivia to know





Yeah, 2. Multiply, add, divide. I've seen enough Vedic math ways to do things that I know my braindead solution could be improved.
I never compare myself with any student from any time other than to say, "I'm still learning." Imagine running into a completely unschooled guy who comes up with this for an approximation of pi?
Srinivasa Ramanujan  Wikipedia[^]
Say WHAT!?
Dang! My '58 Renault Dauphine has another flat tire.





sum of the series (x+n)^2 , 0 <= n <= 4, x=10
= 5(x^2 + 4x + 6) , x=10
= 5(100 + 40 + 6)
= 5(146)
= 730
A contrarian solution to mental arithmetic





I'd say 2 too.
10^2=100
14^2=196
more or less the average of extreme values is (100+196)/2~150
150*5=750
750 must be not so far from the sum of the powers but 750/365~ 2.something
than the reply most probably is 2 (5 secs the whole thing)
modified 3Sep20 2:59am.





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Such an asalt, where they stew in their own juices? Serves them right!! I have a bone to pick with some of these hardboiled politicos: they bite off more than they can chew and then leave their plate for others to clean up.
[edit]: fixed typo
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modified 17Aug20 11:42am.





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Daniel Pfeffer wrote: Isn't it the friars who roast their guests?
... and the Master Of Ceremonies who toasts the guests?





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Today, I tried to use my bluetooth headphones with my laptop.
It's been impossible.
OLD QUESTION
I've noticed bluetooth was not ON in my laptop and tried to start it, but it's been impossible.
Accessed the device administrator and seen Bluetooth wasn't there.
I've connected to the Internet and seen a kind of procedure to solve the issue and I followed the steps...
1. Shown hidden items in the device manager.
2. Uninstall drivers of the bluetooth hidden item.
3. Restart computer to get an automatically updated driver for that device.
Well... After restarting, bluetooth never appeared again.
After restarting it again and seeing a message saying the WIFI card was not accepted, I've opened the back lid, accessed the hardwared, unplugged the card and plugged it again.
Now it works...
I think I will have to buy that new laptop even before I planned to...
Thank you all!
modified 17Aug20 11:03am.





He had my eyetest results so I asked if I could see them.
"Probably not", he said.





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^{And solved in 3... 2... 1...}



