Lonesome-Eight Challenge

[Albert Chan]

Got this from book How to Solve Mathematical Problems (page 132)
Only a single 8, but this is not as hard as it look ...

Code:

              X X 8 X X 
      -----------------
X X X ) X X X X X X X X
          X X X
        -------
            X X X X
              X X X
            -------
                X X X X
                X X X X
               ---------

[pier4r]

what is the operation involved? division?

[ijabbott]

(09-05-2018 10:35 AM)pier4r Wrote:  what is the operation involved? division?

Looks like schoolbook long division notation.

[Massimo Gnerucci]

When I was six I was taught "Column division" the italian way[see here, under Eurasia(!)]: every time I see long division examples everything is in the wrong place.

[Albert Chan]

(09-05-2018 11:26 AM)ijabbott Wrote:  

(09-05-2018 10:35 AM)pier4r Wrote:  what is the operation involved? division?

Looks like schoolbook long division notation.

You guys must be using calculators too much
Yes, this is long division (taught in the fourth-grade ?)

[ijabbott]

Code:


Spoiler alert.










       80809
   _________
124)10020316
     992
    ----
      1003
       992
      ----
        1116
        1116
        ----

[Massimo Gnerucci]

(09-05-2018 02:22 PM)Albert Chan Wrote:  

(09-05-2018 11:26 AM)ijabbott Wrote:  Looks like schoolbook long division notation.

You guys must be using calculators too much
Yes, this is long division (taught in the fourth-grade ?)

Not here, not this way (at least when I was six...)

[Didier Lachieze]

(09-05-2018 11:57 AM)Massimo Gnerucci Wrote:  When I was six I was taught "Column division" the italian way[see here, under Eurasia(!)]: every time I see long division examples everything is in the wrong place.

For me it was the French way, so this challenge doesn't make sense to me...

[Albert Chan]

(09-05-2018 11:57 AM)Massimo Gnerucci Wrote:  When I was six I was taught "Column division" the italian way[see here, under Eurasia(!)]:
every time I see long division examples everything is in the wrong place.

After a peek to the link, I get what you are saying.
With Eurasia rule, the quotient don't line up what is to be subtracted.

[Valentin Albillo]

(09-05-2018 06:09 PM)ijabbott Wrote:  80809
_________
124)10020316
992
----
1003
992
----
1116
1116
----

What part of "lonesome eight" don't you understand ? XD

V.
.

[SlideRule]

from page 55 of Martin Garner's My Best Mathematical and Logic Puzzles.

" 27. In long division, when two digits are brought down instead of one, there must
be a zero in the quotient. This occurs twice, so we know at once that the quotient
is x080x. When the divisor is multiplied by the quotient's last digit, the product is a
four-digit number. The quotient's last digit must therefore be 9, because eight times
the divisor is a three-digit number.
The divisor must be less than 125 because eight times 125 is 1,000, a four-digit
number. We now can deduce that the quotient's first digit must be more than 7, for
seven times a divisor less than 125 would give a prod uct that would leave more
than two digits after it was subtracted from the first four digits in the dividend. This
first digit cannot be 9 (which gives a four-digit number when the divisor is multiplied
by it), so it must be 8, making the full quotient 80809.
The divisor must be more than 123 because 80809 times 123 is a seven-digit number
and our dividend has eight digits. The only number between 123 and 125 is 124."

BEST!
SlideRule

[Albert Chan]

(09-05-2018 08:30 PM)SlideRule Wrote:  from page 55 of Martin Garner's My Best Mathematical and Logic Puzzles.

The divisor must be more than 123 because 80809 times 123 is a seven-digit number
and our dividend has eight digits. The only number between 123 and 125 is 124.

FYI, the book How to Solve Mathematical Problems do not need to do 123 * 80809
The author, Wagne A. Wickelgren, noted what is subtracted must be 990 to 999.
So, 123 * 8 = 1000 - 16 < 990 is enough to reject it.

[SlideRule]

M Gardner is credited w an extensive list of math/logic puzzle books, articles etc. This is neither his first nor his only errata as even a modest search will confirm same. For example:
Martin Gardner’s Mistake
Tanya Khovanova
MIT
January 10, 2013
For my part, the reasoning behind the quick determination of the ZERO holders was the key take-away for those struggling with the deployed methodology of division. Good eye, apropo commentary!

BEST!
SlideRule

[pier4r]

(09-05-2018 02:22 PM)Albert Chan Wrote:  You guys must be using calculators too much
Yes, this is long division (taught in the fourth-grade ?)

No simply when I do division I never use a second number to subtract from. So I am not used to the layout.

[Valentin Albillo]

(09-06-2018 10:28 AM)pier4r Wrote:  

(09-05-2018 02:22 PM)Albert Chan Wrote:  You guys must be using calculators too much
Yes, this is long division (taught in the fourth-grade ?)

No simply when I do division I never use a second number to subtract from. So I am not used to the layout.

Same here, we don't use that weird layout though I did recognize it was so-called "long division" (called simply "division" where I live).

Seems A. Chan thought that this challenge's layout is universal, thus the patronizing tone. Not so.

V.
.

[Albert Chan]

Hi, Valenin Albillo

I thought they are pulling my legs (Eurasia rule ?)

Never know there are so many different ways to write long divisions.

I am most impressed with the Mexico way, where what is subtracted is not written down.
All is done in the head, only result is written down, like this:

Code:

       80809
   _________
124)10020316
      1003
        1116
           0

[Massimo Gnerucci]

(09-08-2018 10:12 PM)Albert Chan Wrote:  I thought they are pulling my legs (Eurasia rule ?) :)

Pulling your leg?!? :P
Hey, it's not me who wrote that Wikipedia article.

[pier4r]

(09-08-2018 10:12 PM)Albert Chan Wrote:  Hi, Valenin Albillo

I thought they are pulling my legs (Eurasia rule ?)

Actually I quite don't understand any of the layouts. I was taught and I always did/do as follows.

Code:



spoiler









10020316 | 124
  10       8  (1st operation)
  100      80  (2nd op)
    11     808 (3rd op)
    111    8080 (4th op)
       0   80809 (5th op)

So the divisor is on the right not on the left. Of course one can save the writing down of the quotient, writing it in one line. I wrote it in multiple lines to show the progression.

[ijabbott]

(09-09-2018 09:56 AM)pier4r Wrote:  

(09-08-2018 10:12 PM)Albert Chan Wrote:  Hi, Valenin Albillo

I thought they are pulling my legs (Eurasia rule ?)

Actually I quite don't understand any of the layouts. I was taught and I always did/do as follows.

Code:



spoiler









10020316 | 124
  10       8  (1st operation)
  100      80  (2nd op)
    11     808 (3rd op)
    111    8080 (4th op)
       0   80809 (5th op)

So the divisor is on the right not on the left. Of course one can save the writing down of the quotient, writing it in one line. I wrote it in multiple lines to show the progression.

So, like the Mexican layout, if you have difficulty doing the subtractions (to obtain the remainders at each step) in your head, you have to do them "out of shot" on a separate bit of paper? The English long division method does the subtractions "in shot".

[ijabbott]

Although putting the divisor on the left, followed by )‾‾ seems a bit strange, it can be read in English as "go(es) into".