I like calculator quirks like this. I remember as a kid playing with the number pad and noticing a geometric center of mass in number sequences
┌───┬───┬───┐
│ 7 │ 8 │ 9 │
├───┼───┼───┤
│ 4 │ 5 │ 6 │
├───┼───┼───┤
│ 1 │ 2 │ 3 │
├───┼───┼───┤
│ 0 │ . │ │
└───┴───┴───┘
The even simpler example is more striking imo.
(147 + 369) / 2 = 258
and
(741 + 963) / 2 = 852
But this is obvious?
(741 + 963)/2 = (700+900)/2 + (40+60)/2 + (1+3)/2, it's just average in each decimal place.
Obvious now and really cool in hindsight.
The decimal digits clearly have a conspiracy going on.
That would work in any base, I even think we would find way more interesting coincidences in base 12 (as Sumerians preferred), because it's divisible by 2,3,4,6.
It's unfortunate that we have 5 fingers.
If you count the sections of your four fingers with your thumb, you can count up to 12 on one hand!
I have always counted to 20 on one hand. even as a kid. base, lower joint, upper joint, top. times 5 - including the thumb: my motor memory is trained so that i switch seamlessly from keeping the curse on top of the finger using my thumb, and then, once i cross 16, switch to using the index finger to "cursor" the thumb.
Same here. I have always counted 20 on one hand, so 40 with both. That's how my parents taught me to count when I was little. I used this method so often as a kid that, even though I don't count like this anymore, every number up to 40 still has its own place on my fingers.
It was only as an adult that I realised nobody around me counted this way. You are the first person I have found who talked about this method, so I am glad to find this comment of yours.
If you count with each finger as a binary digit you can count up to 15 on one hand!
255 if you use both hands!
More like 1023 if you also use thumbs but I prefer to use them as carry, overflow bits.
I trained myself to do this by default a very long time ago and I can't imagine counting any other way.
It's so natural, useful and lends well to certain numerical tricks. We should explicitly be teaching binary to children earlier.
I am French and we cont extending our fingers from a closed fist. Typically to 2x5=10.
When I was a kid I relized that I can count the fives on the right hand (1 finger for each 5 on the left), which brought me to 25.
It is only when I was traveling in Asia and watched people on markets that I realized that I can use my thumb to count my 12 other finger phalanges, which brought the total to 144. You just need to know your multiplication table of 12 :)
A system I read about uses the thumb for 5, so that each hand can count (thumb down) 0..4 (thumb up) 5..9.
This gives you the range 0..99. Sweeet.
i remember the 1110 thing on a calc as well.
741 + 369 & 963 + 147 | 123 + 987 & 321 + 789 (left right | up down)
159 + 951 & 753 + 357 | 258 + 852 & 456 + 654 (diagonally | center lines)
the design of a keypad... it unintentionally contains these elegant mathematical relationships.
i call this phenomena: outcomes of human creations can be "funny and odd", and everybody understand that eventually there will be always something unpredictable.
ita intuited knowledge, which is only later understood. (itzhak bentov, stalking the wild pendulum)
14789 + 36987 / 2 would do the same thing. Why trace back?
So would 147 and 369. As it’s just an average, per digit, I’m not sure this is very interesting.
Being curious is delightful.
[dead]
Just to show that you could - 14861 and 36843 gives 25852
Great, now I'm getting Carrot Top flashbacks. "Dial right down the center of the phone!"
For non-Americans and/or those too young to remember when landline service was still dominant, in the 90s and early 2000s AT&T ran a collect-call service accessible through the number 1-800-CALL-ATT (1-800-225-5288) and promoted it with ads featuring comedian Carrot Top. And if you don't know who Carrot Top is, maybe that's for the best.
now there's some solid ascii, great work sir
how did you submit this table in HN??
Use two or more spaces at the beginning of a line and it will be formatted as code ("<code>") and then use symbols as you like.
https://news.ycombinator.com/formatdoc