Re: [math-fun] A + B + C = D and A, B, C substrings of D
I don't understand how you add up 1820 from 3 of its substrings. The available substrings are 1 2 8 18 20 82 182 820. one of them has to be as big as 1820/3=606 -- that's 820. One of the 2 remaining has to be as big as (1820-820)/2=500. That's also 820. The third has to be 1280-820-820=180, which isn't one of the choices. On Tue, Feb 25, 2020 at 12:10 PM Michael Greenwald <mbgreen@seas.upenn.edu> wrote:
On 2020-02-25 10:28, Tom Duff wrote:
I should say, I excluded 0 as an addend, because then you get a=a+0+0 for every a with a zero in it, which strikes me as not interesting.
Adding 0's to a previous solution is also uninteresting. I assume you meant to cut those out, too, but you (mistakenly?) included all forms of 150* = 50* + 50* + 50* (but almost no other examples [e.g. 182, 1820, 18200, ...], although you do include 195000=5000+95000+95000 and 19500, and 195 = 5 + 95 + 95)
Not "as big as (1820-820)/2=500', but "as big as 1820-820=1000". The rest is correct (according to me). On Tue, Feb 25, 2020 at 2:28 PM Tom Duff <td@pixar.com> wrote:
I don't understand how you add up 1820 from 3 of its substrings. The available substrings are 1 2 8 18 20 82 182 820. one of them has to be as big as 1820/3=606 -- that's 820. One of the 2 remaining has to be as big as (1820-820)/2=500. That's also 820. The third has to be 1280-820-820=180, which isn't one of the choices.
On Tue, Feb 25, 2020 at 12:10 PM Michael Greenwald <mbgreen@seas.upenn.edu> wrote:
On 2020-02-25 10:28, Tom Duff wrote:
I should say, I excluded 0 as an addend, because then you get a=a+0+0 for every a with a zero in it, which strikes me as not interesting.
Adding 0's to a previous solution is also uninteresting. I assume you meant to cut those out, too, but you (mistakenly?) included all forms of 150* = 50* + 50* + 50* (but almost no other examples [e.g. 182, 1820, 18200, ...], although you do include 195000=5000+95000+95000 and 19500, and 195 = 5 + 95 + 95)
Ignore the correction, it was right in the first place. I'm done faking myself out now (I wish). On Tue, Feb 25, 2020 at 2:30 PM Tom Duff <td@pixar.com> wrote:
Not "as big as (1820-820)/2=500', but "as big as 1820-820=1000". The rest is correct (according to me).
On Tue, Feb 25, 2020 at 2:28 PM Tom Duff <td@pixar.com> wrote:
I don't understand how you add up 1820 from 3 of its substrings. The available substrings are 1 2 8 18 20 82 182 820. one of them has to be as big as 1820/3=606 -- that's 820. One of the 2 remaining has to be as big as (1820-820)/2=500. That's also 820. The third has to be 1280-820-820=180, which isn't one of the choices.
On Tue, Feb 25, 2020 at 12:10 PM Michael Greenwald <mbgreen@seas.upenn.edu> wrote:
On 2020-02-25 10:28, Tom Duff wrote:
I should say, I excluded 0 as an addend, because then you get a=a+0+0 for every a with a zero in it, which strikes me as not interesting.
Adding 0's to a previous solution is also uninteresting. I assume you meant to cut those out, too, but you (mistakenly?) included all forms of 150* = 50* + 50* + 50* (but almost no other examples [e.g. 182, 1820, 18200, ...], although you do include 195000=5000+95000+95000 and 19500, and 195 = 5 + 95 + 95)
On 2020-02-25 14:28, Tom Duff wrote:
I don't understand how you add up 1820 from 3 of its substrings.
Good that you didn't understand, because I was totally wrong. Adding and stripping 0's from each of the strings of digits works when all of A, B, and C are suffixes of D. I was magically imagining that unbounded sequences of 0's were available inside of D. Doh.
The available substrings are 1 2 8 18 20 82 182 820. one of them has to be as big as 1820/3=606 -- that's 820. One of the 2 remaining has to be as big as (1820-820)/2=500. That's also 820. The third has to be 1280-820-820=180, which isn't one of the choices.
On Tue, Feb 25, 2020 at 12:10 PM Michael Greenwald <mbgreen@seas.upenn.edu> wrote:
On 2020-02-25 10:28, Tom Duff wrote:
I should say, I excluded 0 as an addend, because then you get a=a+0+0 for every a with a zero in it, which strikes me as not interesting.
Adding 0's to a previous solution is also uninteresting. I assume you meant to cut those out, too, but you (mistakenly?) included all forms of 150* = 50* + 50* + 50* (but almost no other examples [e.g. 182, 1820, 18200, ...], although you do include 195000=5000+95000+95000 and 19500, and 195 = 5 + 95 + 95)
participants (2)
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Michael Greenwald -
Tom Duff