Digital Calendar

Question

Given a date, output the X and Y position of the current day of the date on a digital calendar. The digital calendar is sort of the calendar that gets shown when you click on your computers clock (at least on windows), and it looks something like this:

If we assume that the given date is 25.09.2017, the result would be (2,5), because the 25th day of the 9th month of this year is in the second column and fifth row.

Note that if the date would be something like 29.08.2017, we couldn't use the calendar from above, but a new one for August. The gray-ish numbers are simply there to fill the gaps until the day that the month actually starts.

Input

A date, in any reasonable format.

Output

The point or coordinates that the day of the given date lies at, in its respective calendar. These should be 1-indexed.

Rules

• This is code-golf, the shortest code in any language wins.
• Standard loopholes are forbidden.

Additional Notes

The first column of the calendar will always be Sunday.

Here are the digital calendars from January and September 2017:

Test Cases

Input: 06.02.2018 (DD.MM.YYYY) or 2018.02.06 (YYYY.MM.DD)
Output: (3,2)

Input: 12.11.1982 (DD.MM.YYYY) or 1982.11.12 (YYYY.MM.DD)
Output: (6,2)

Input: 01.01.2030 (DD.MM.YYYY) or 2030.01.01 (YYYY.MM.DD)
Output: (3,1)

Input: 13.06.3017 (DD.MM.YYYY) or 3017.06.13 (YYYY.MM.DD)
Output: (6,3)

Answer 1

Mathematica, 83 bytes

New Rules:Starting on Sunday

{s=Min@Position[(d=DayName)@{6,1,#}&/@Range@7,d@DateObject@{##}],⌈(#3-s)/7⌉+1}&   

-5 bytes from @Misha Lavrov

Input form

[2030, 1, 1]
yyyy-mm-dd

Answer 2

JavaScript (ES6), 64 59 bytes

f=
(s,d=new Date(s),e=d.getDay())=>[1+e,(d.getDate()-e)/7+2|0]

<input oninput=o.textContent=f(this.value)><pre id=o>

Input is any string which JavaScript recognises as a date. Save 16 bytes if a JavaScript date object is acceptable input. Edit: Saved 5 bytes thanks to @GrzegorzOledzki.

Answer 3

TI-Basic (84+), 27 bytes (50 characters)

:Prompt Y,M,D
:dayOfWk(Y,M,D
:{Ans,2+int(7⁻¹(D-Ans

Answer 4

Python 2, 109 98 bytes

The datetime module docs are 50,000 bytes, so I'm not using the datetime module yet.

def f(d,m,y):t=m<3;y-=t;Y=y%100;W=(d+(13*m+156*t-27)/5-y/100*2+y/400+Y+Y/4)%7+1;print W,(d+13-W)/7

Try it online!

My formula to compute day of week comes from https://cs.uwaterloo.ca/~alopez-o/math-faq/node73.html.

The formula is as follows (converted from image to text):

W = (k + floor(2.6*m-0.2) - 2*C + Y + floor(Y/4) + floor(C/4)) mod 7

where floor(k) denotes the integer floor function

k is day (1 to 31)

m is month (1 = March, ..., 10 = December, 11 = Jan, 12 = Feb) Treat Jan & Feb as months of the preceding year C is century (1987 has C = 19)

Y is year (1987 has Y = 87 except Y = 86 for Jan & Feb)

W is week day (0 = Sunday, ..., 6 = Saturday)

Here the century and 400 year corrections are built into the formula. The floor(2.6*m-0.2) term relates to the repetitive pattern that the 30-day months show when March is taken as the first month.

The row number can be calculated as one more than the number of Sundays in the month preceding the day.

-7 bytes thanks to @GrzegorzOledzki