For summing a set of numbers like this, like for splitting a restaurant bill, almost everyone I know either goes “just split it down the middle, it’s fine” or else pulls out their calculators/phones. Same with board game nights.
I take it there are people who try to do it in their heads? Maybe a generational difference? It’s a lost skill to people my age and younger…
Yep, and that’s what my wife does to me when I’m counting. Speaks it out. But I might be doing it in a different order.
I have to stop, and start again. She apologizes, and stops. Or, I just let her count. Excuse me - ADD.
I look at that and think (38 x 20) - 38
760 - 38
722
Sometimes I group numbers when adding them, but usually I just add them left to right.
I would say 8, 13, 17, 19, 20, 27 as I mentally added each number to the total.
I don’t either. I count up from where I am. So 187+100 is less than 332 but 187+200 is more, so I start with 100. Approx. 80 to (1)30 is about 50, so I know the answer is close to 150. Then I narrow down 87 to 37 would be 50 so 87 to 32 is 5 less than that, or 145. It gets me the answer very quickly with just a few comparisons and not a lot of formal plugging through the actual math.
To me, 38x19 is 40x19 - 2x19. 40x19 is easy enough to do in my head (19 doubled then doubled again, then add a zero to multiply by 10, so it’s 760). Now just subtract 38 from 760 which is easier to subtract 40 from 760 (720) and add 2. So the answer is 722. Very quick and easy to do in my head.
That’s us. “Whatever”
That’s not us. While we don’t keep ‘track’ of win/lose, we are both competitive and cheer each other on. My wife was an IronMan, never had a prayer to win, just hoping to finish and not go to the hospital (again). I was her sherpa, so of course we cheer each other on in everything we do. Even when we compete against each other.
I know I’m getting off track, but it’s my thread. I was surprised to find that my wife wanted me to teach her to play chess. I mentioned to my mom that I didn’t know how competitive she was, my mom looked at me and said “She’s an IronMan, what would you expect?”
Heh. Yeah. Running some numbers, and I don’t have any hard data, we play at least 12 games of chess a week. for 7 years now… So over 4000 games. It took my wife ~100 games before she beat me. She stuck with it. That’s the IronMan in her.
You couldn’t ask for a better person to be on your side.
Same here with cribbage. Let’s say I got 12 points. I count 5 then 5 then 2. The board is segmented by 5, so if I’m starting from the second point in a block of five, I jump to the next second point, then the next second point after that, then add 2.
My wife will count to the first point in the next block, then jump to the next block, then add the remainder. She would count 4 then 5 then 3.
Your way is the same as what I’d do if I needed the exact number.
But if a decent estimate is as good as the actual, then 40x20 & back off a bit less than 10% gives a reasonable estimate with even less mental effort.
That’s what I do. And cribbage is a very, very strange game. Just saying…
Yeah, sometimes you just have to do that. But as it’s said, “Close only counts in horseshoes and hand grenades” 
But yeah, when there is no real way to know how much… gravel to order, you can only try to get close.
If by unique you mean that no one prime may be repeated in the sequence, we’re getting into some rather interesting number theory.
If repeats are allowed it’s uninteresting, of course: any even number can be expressed as a sum of multiple 2s. And any odd number by starting with 3 followed by multiple 2s.
But if we require that each prime may appear only once in the sum, I’m not sure if there is a theorem (like the fundemental theorem of arithmetic for product decomposition) for sums?
Input from real mathematicians welcome here! This seems to relate to Goldbach’s conjecture, which is unproven.
All replies welcome and interesting. But you just broke my brain. I’m gonna go grocery shopping. That I can handle.
There are people who will shave seconds or fractions of seconds off the time it takes to, say, do addition differently… all purportedly in the interests of saving time. Yet I wager some of these very same people will sit through an entire goddam red light when there’s hardly any traffic and THEN turn right only when it changes to green when they could have turned five times while it was still red and not wasted a full minute or more of their life just sitting there.
The nature of my job before it all went computerized was lots and lots of mental arithmetic while also busy with other cognitive and physical tasks under time pressure.
Whether you estimated 40 or computed 37 made zero difference in the outcome, but the estimate left a lot more “brain bytes” for stuff that mattered more. So estimating almost “by eye” without resorting to arithmetic at all was a good skill to develop.
Turn on red depends on where you live. It’s not legal in the UK, for example… took me a little while to get used to it when I moved to the US. Not sure if it’s allowed in all US states, for that matter?
And a full minute of each and every person lined up behind them to turn right.
IMO you (any you) are free to dawdle away as much of your life as I want. You have zero right to do that to anyone else, much less multiple anyone elses.
You’re entitled to the space and time an efficient driver would use and no more. I’m not more important than you are. Not less important either. We all owe the people around us heads-up “drive like you mean it” driving. All the time.
This.
I think you and I should go bowling sometime.
I hate it when people do this, but I also remember they’re not required to turn on red, so I don’t honk (and I hate honkers even more.) I’m not driving to an emergency so losing a minute sitting at a red is no big deal. Leaves me better mentally than stewing at the guy ahead of me.
I hope you bowl quickly. 
Honkers that are far enough back in line that they can’t see whether the first car is waiting for a pedestrian, or u-turners, or an approaching ambulance, or whatever piss me right off too. But if I can see there’s no obstacles and they’re simply daydreaming or phoning phiddling they’ll often get a gentle wake-up toot, not a “F*** You!” New Jersey long blare.
Some people here just won’t turn on red and it doesn’t have to with distractions. I’ve seen others more than once honk at someone on red repeatedly and the person refused to move until the light turned green. We were also explicitly taught in high school that we are not required to turn right on red, only if it’s safe to do so (obv) and if we want to. It’s rare to encounter such a driver that doesn’t want to—often they are either from out of state or elderly—but it does happen. I personally get more annoyed at the people who refuse to enter the intersection to wait to make a turn and instead wait behind the stop line, but I try my best to shake it off. (And I believe in other jurisdictions, you can’t do this.) I always leave enough time so I don’t feel I’m in a hurry to where I’m going. That’s how accidents (and high blood pressure) happen.
I believe you’re talking about the typical left turn? That too is a pet peeve of mine.
I’ve never heard of it being illegal anywhere, but it sure could be.
Yeah, sorry. I forgot the left part of the turn. This behavior is far more common than not turning on red. There are sone intersections where it’d be nigh impossible to turn left if you didn’t enter the intersection and wait for the light to change.