patrick.net

komputodo says

how can it be 19? By that reasoning, a+b+c+d+b+c+d+c+d+d would equal 6666 but it doesn't...It equals 51.

Would you prefer the question to be:


  A * 1000 + B * 100 + C * 10 + D
           + B * 100 + C * 10 + D
                     + C * 10 + D
                              + D
---------------------------------
  6 * 1000 + 6 * 100 + 6 * 10 + 6 = 6666


Then: "what is A+B+C+D?"

That's the real question. I think. It is poorly worded, and it has two solutions, and if I used normal mathematical notation, that's not the question, and if I use normal mathematical notation, there is no solution, at least for integers and if I don't use integers, there's an infinite number of solutions.

richwicks says

komputodo says

how can it be 19? By that reasoning, a+b+c+d+b+c+d+c+d+d would equal 6666 but it doesn't...It equals 51.

Would you prefer the question to be:


  A 1000 + B 100 + C 10 + D
+ B 100 + C 10 + D
+ C 10 + D
+ D
-------------------------------
6 1000 + 6 100 + 6 * 10 + 6


Then: "what is A+B+C+D?"

That's the real question. I think. It is poorly worded, and it has two solutions, and if I used normal mathematical notation, that's not the question, and if I use normal mathematical notation, there is no solution, at least for integers and if I don't use integers, there's an infinite number of solutions.

I think the question is just fine how it is written. It just seems to me that people are trying to overcomplicate it and that they have forgotten elementary school math.

komputodo says

I think the question is just fine how it is written. It just seems to me that people are trying to overcomplicate it and that they have forgotten elementary school math.

Show your work.

Maybe I am entirely misunderstanding the question.

Oh - I think I see the problem - where do you come up with this equation:

a+b+c+d+b+c+d+c+d+d

? I think that's where the discrepancy lies, and also, I don't agree this is a well worded question, because it has 2 solutions.

richwicks says

Oh - I think I see the problem - where do you come up with this equation:

a+b+c+d+b+c+d+c+d+d

?

to simplify, lets do

its not 2+4+4...its 24 + 4

richwicks says

I don't agree this is a well worded question, because it has 2 solutions.

I didn't see where it stated that there was only 1 solution

richwicks says

You must have misunderstood the question. It's asking:

ABCD +
 BCD +
  CD +
   D
----
6666

in my mind abcd = 6319 meaning a=6000, b=300, c=10 , d=9...bcd = 319, cd=19, d=9....total 6666

richwicks says

SunnyvaleCA - that Python?

Yes python. However, the asterisk symbol, designating multiplication in Phython, is treated as toggling bold text on and off due to the HTML "markdown" feature. I really am liking python for small tasks: very straightforward syntax, lots of examples out there on the internet, and fantastic built-in and 3rd party libraries.

As an example of 3rd party libraries... My girlfriend had a 500 page book with the binding cut off and a self-feeding scanner that produced PDF scans but only 1-sided. She wanted a single PDF with all the pages in order. I had her scan all the pages using the automatic sheet feeder, flip the stack upside down and scan them all again. By the time that was done I had a python script that used a free 3rd party PDF utilities library to reverse the second set of pages and then interleve them with the first set. Done!

stereotomy says

It's one equation with three unknowns. By the most elementary principles of linear algebra, this is a singular matrix, which necessarily has no unique solution.

Actually, it's 4 unknowns, but yeah. There are an infinite number of solutions except for the fact that you are constrained to integers between 1 and 9. That happens to limit it to 2 solutions.

Onvacation says

That's cheating! You're supposed to do it in your head!

I'm working smarter, not harder.

I believe everyone is overthinking it.

A=6000
B= 300
C= 20
D= 1.5

Answer:6321.5

Yep, I'll put $ on it.

Nobody said we needed to use base 10. How about bases 7 through 16. (Has to be at least base 7 because otherwise you can't write 6666 as the answer.

digits = "0123456789ABCDEF"
for base in range(6,16+1):
    for a,b,c,d in itertools.product(range(0,base),repeat=4):
        if a*base**3+b*base**2+c*base+d + b*base**2+c*base+d + c*base+d + d == (((6*base+6)*base+6)*base+6):
            print(base,
, digits[a],digits[b],digits[c],digits[d],
,a+b+c+d)

7  6 2 6 5  19
10  5 8 1 9  23
10  6 3 1 9  19
11  5 8 5 7  25
13  6 2 A 8  26
14  5 9 B 5  30
14  5 A 1 C  28
14  6 2 B 5  24
14  6 3 1 C  22

Interpreting the last line of output as an example: in base 14, the numbers for a,b,c,d are 6,3,1,C and the sum of those is 22 (in base 10).

^^^ the "pre" tag worked great. I also searched for * and replaced with * .

komputodo says

richwicks says

Oh - I think I see the problem - where do you come up with this equation:

a+b+c+d+b+c+d+c+d+d

?

to simplify, lets do

its not 2+4+4...its 24 + 4

yes, and 2+4 = 6

It's adding the digit of each column together. What number do you think it ought to be?

SunnyvaleCA says

Yes python. However, the asterisk symbol, designating multiplication in Phython, is treated as toggling bold text on and off due to the HTML "markdown" feature.

Yeah, you can write the symbol (once) by escaping out the ascii character sequence in html, but when you go to edit it, it turns into the ascii symbol. If you really want me to demonstrate it, ask because I have to escape out symbols to demonstrate, and I'm just up in the middle of the night for a few minutes.

richwicks says

komputodo says

richwicks says

Oh - I think I see the problem - where do you come up with this equation:

a+b+c+d+b+c+d+c+d+d

?

to simplify, lets do

its not 2+4+4...its 24 + 4

yes, and 2+4 = 6

It's adding the digit of each column together. What number do you think it ought to be?

I think the reason that we disagree is because when I see a number like 24, i think of it as 20+4 and you think of it as a 2 and a 4...when i saw the number 6666, I saw 6 thousand, 6 hundred and sixty six. and you saw 4 sixes

komputodo says

richwicks says

komputodo says

richwicks says

Oh - I think I see the problem - where do you come up with this equation:

a+b+c+d+b+c+d+c+d+d

?

to simplify, lets do

its not 2+4+4...its 24 + 4

yes, and 2+4 = 6

It's adding the digit of each column together. What number do you think it ought to be?

I think the reason that we disagree is because when I see a number like 24, i think of it as 20+4 and you think of it as a 2 and a 4...when i saw the number 6666, I saw 6 thousand, 6 hundred and sixty six. and you saw 4 sixes

??

   A
+ BA
----
  28

What is A+B?

What would your answer be in this case? Show your work. I don't understand what you don't understand.

richwicks says

I think the reason that we disagree is because when I see a number like 24, i think of it as 20+4 and you think of it as a 2 and a 4...when i saw the number 6666, I saw 6 thousand, 6 hundred and sixty six. and you saw 4 sixes

??

   ``A
+ BA
-------
  28

What is A+B?

What would your answer be in this case? Show your work. I don't understand what you don't understand.
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I see it as 24...if B is 2x10 and a is 4x1, then is B=2 or B=20?

komputodo says

I see it as 24...if B is 2x10 and a is 4x1, then is B=2 or B=20?

B = 2. Just 2. It's not 20, it's not 2x10, it's just a digit between 0 and 9, and in this case, it's 2

richwicks says

komputodo says

I see it as 24...if B is 2x10 and a is 4x1, then is B=2 or B=20?

B = 2. Just 2. It's not 20, it's not 2x10, it's just a digit between 0 and 9, and in this case, it's 2

so 6666 is not 6 thousand, six hundred and sixty six? its just 4 sixes in a row?

komputodo says

richwicks says

komputodo says

I see it as 24...if B is 2x10 and a is 4x1, then is B=2 or B=20?

B = 2. Just 2. It's not 20, it's not 2x10, it's just a digit between 0 and 9, and in this case, it's 2

so 6666 is not 6 thousand, six hundred and sixty six? its just 4 sixes in a row?

A is a single digit between 0 and 9
B is a single digit between 0 and 9
same with C and D

6666 is 6 thousands, size under and sixty six. But if you were to write "6666 = WXYZ", W=6, X=6, Y=6, Z=6.

What's the answer:

UkraineIsTotallyFucked says

What's the answer:

It is either 1 or 25, most likely 1. I see that each section multiplied by the 5 in the middle equal the number on the opposite side.