I was wrong in my first attempt to generalise the problem. I’d said:
a + b * i, where a and b are integer scalars, and i is an integer vector,
i0,i1,i2...,
which is correct, but not sufficient.
The Quora problem also requires, or perhaps just implies, that i’s elements are
“proportional”, ie c = i0 % i1 = i2 % i3 for some c.
So, i = 1 2 3 6 is ok.
However, i = 2513 1777 1125 3997 6 only meets my earlier criterion, not the
proportionality requirement.
I suppose our interpretation of “proportional” was at fault. I’d thought at
first that it just applied to my constant factor b, but c also needs to be
satisfied.
Cheers,
Mike
> On 16 Aug 2018, at 02:06, Raul Miller <[email protected]> wrote:
>
> Yes, well...
>
> Consider this sequence:
> 7541 5333 3377 11993 20
>
> Thanks,
>
> —
> Raul
>
> On Wednesday, August 15, 2018, Jose Mario Quintana <
> [email protected]> wrote:
>
>>> I do not see any attempt in the question at generalizing—so technically
>> the
>>> answer would be a number.
>>
>> In addition, that number presumably should be a function of the four
>> numbers; as far as I can see, that function can be defined as the verb,
>>
>> v=. (-/ .* % -/ .+)@:(2 2&$)
>>
>> So,
>>
>> v 21 38 55 106
>> 4
>>
>> In the Quora page, there are "Related Questions" and the answers to those
>> questions according to v are,
>>
>> v 41 56 36 48
>> 16
>> v 18 78 19 83
>> 3
>> v 23 30 57 78
>> 6
>>
>>> But I expect that easy to describe (but accurate) general approaches
>> would
>>> fit right in...
>>
>> All the numbers (and the answers) in the examples above are positive
>> integers; however, v still seems to work fine when they are not; for
>> example,
>>
>> v 23 30 57 78 + 0.5
>> 6.5
>> v 23 30 57 78 * 0.5
>> 3
>> v %: 23 30 57 78
>> 1.67100218
>> v %: 23 30 , - 57 78
>> 0.610353598j_0.324426817
>> v 4j5 5j6 3j5 3j6
>> 3j4
>>
>> Moreover, v produces an answer when there are a lot of possible answers (in
>> principle, a continuum),
>>
>> v 1 2 1 2
>> 0
>>
>> including, a "limit" answer when there is no (conventional) answer,
>>
>> v 2 4 0 2
>> _
>>
>> v 1 2 3 4 j. 5 6 7 8
>> 0j_
>>
>>
>> On Tue, Aug 14, 2018 at 7:42 PM, Raul Miller <[email protected]>
>> wrote:
>>
>>> I do not see any attempt in the question at generalizing—so technically
>> the
>>> answer would be a number.
>>>
>>> But I expect that easy to describe (but accurate) general approaches
>> would
>>> fit right in...
>>>
>>> Thanks,
>>>
>>> —
>>> Raul
>>>
>>> On Tuesday, August 14, 2018, Jose Mario Quintana <
>>> [email protected]> wrote:
>>>
>>>> After I saw your message I searched for the particular Quora problem
>> and
>>>> this is what I found,
>>>>
>>>> https://www.quora.com/What-number-must-be-subtracted-
>>>> from-21-38-55-and-106-each-so-that-the-remainders-
>>>> technically-differences-are-proportional
>>>>
>>>> It seems to me that the shape of the array is restricted to be exactly
>> 4
>>>> and the numbers do not have to be integers. Am I wrong?
>>>>
>>>>
>>>> On Tue, Aug 14, 2018 at 7:00 PM, 'Mike Day' via Programming <
>>>> [email protected]> wrote:
>>>>
>>>>> It should work on arrays of the form
>>>>> a + b * i, where a and b are integer scalars, and i is an integer
>>>>> vector.
>>>>> So, if
>>>>> q=: 6 + 7*1 2 5 11 23,
>>>>> applying this function yields
>>>>> (-/ .* % -/ .+)@:(2 2&$) q
>>>>> 7.4
>>>>> I think you need instead something like
>>>>> Difference’s greatest common divisor,
>>>>> dgcd =: +./@:(2 -~/\ ])
>>>>> So
>>>>> dgcd q
>>>>> 7
>>>>>
>>>>> It’s a bit more complicated to recover the factors, 1 2 5 ..., which
>>> seem
>>>>> to be required in the Quora problem:
>>>>> (](([-|~)%])dgcd) q
>>>>> 1 2 5 11 23
>>>>> This works for the original array, too,
>>>>> (](([-|~)%])dgcd) 21 38 55 106
>>>>> 1 2 3 6
>>>>>
>>>>> And
>>>>> dgcd 21 38 55 106
>>>>> 17
>>>>>
>>>>> Sorry for any formatting problems - typing on iPad,
>>>>>
>>>>> Mike
>>>>>
>>>>>
>>>>> Please reply to [email protected].
>>>>> Sent from my iPad
>>>>>
>>>>>> On 14 Aug 2018, at 23:18, Jose Mario Quintana <
>>>>> [email protected]> wrote:
>>>>>>
>>>>>> (-/ .* % -/ .+)@:(2 2&$)21 38 55 106
>>>>> ------------------------------------------------------------
>> ----------
>>>>> For information about J forums see http://www.jsoftware.com/
>> forums.htm
>>>>>
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