Question

For the year 2015, determine the following:
a) the calendar dates on which Mondays will occur in March.
b) the months in which the 13th will fall on a Friday.

Answer 1

2 9 16 23 30

Answer 2

lol you sure you didnt look at calendar ?

Answer 3

ugh i wiSH ALL THE MONTHS HAD THE SAME NUMBER OF DAYS

Answer 4

no i did lol

Answer 5

okay i believe you :) if each month has same number of days, then i guess summer wont come in the same month each year haha

Answer 6

thats not a typo i did look at the calender

Answer 7

(...) By the 16th century, the accumulating inaccuracy caused the vernal equinox
(the first day of Spring) to fall on March 11 instead of its proper day, March 21.
The calendar's inaccuracy naturally persisted throughout the year, but at this season
it meant that the Easter festival was celebrated at the wrong astronomical time.
Pope Gregory XIII rectified the discrepancy in a new calendar, imposed on the
predominantly Catholic countries of Europe. He decreed that 10 days were to be
omitted from the year 1582, by having October 15 of that year immediately follow
October 4. At the same time, the Jesuit mathematician Christopher Clavius amended
the scheme for leap years: these would be years divisible by 4, except for those
marking centuries. Century years would be leap years only if they were divisible by
400.

Answer 8

it is fascinating how calendar was really a big deal in those days xD

Answer 9

@ganeshie8 lol is srsly intelligent

Answer 10

not rly but thank you @sumanta <3

Answer 11

Jan- 31, 23=Friday
feb 28
march 31

Answer 12

31=Friday

Answer 13

Feb28 is sunday then

Answer 14

wait

Answer 15

@ganeshie8 Back then Calendars and Candles were big on the market. Similar todays IPhones and 3d TV's xD

Answer 16

oh saturday is 31st

Answer 17

i think feb month is a pain in the neck for working calendar problems

we can ease the pain by pretending that the year starts with March instead

Answer 18

but then in july and aug its 31 31

Answer 19

lol true @Joel_the_boss good old days enjoyed by our great forefathers !

Answer 20

or i think we shud just chuck

Answer 21

the months and keep 52 weeks

Answer 22

52*

Answer 23

12, 13s

Answer 24

yeah having somethign concrete to play wid is a good start xD

today is jan23, friday.
also assigning numbers to days might open other ways to approach these problems in general :
```
0 -> sunday
1 -> monday
2 -> tuesday
3 -> wednesday
4 -> thursday
5 -> friday
6 -> saturday
```

Answer 25

and writing out all those 30s and 31s in order

Answer 26

or by remainders of 7
starting from jan

Answer 27

jan-3
feb-0
3
2
3
2
3
3
2
3
2
3

Answer 28

interesting xD
so looks like a 30 day month advances by 2
a 31 day month advances by 3

Answer 29

im trying to see if there is a better way to put this to gether

Answer 30

like there is lots of recursion here

Answer 31

im seeing if we can think of it as a big matrix and applying transformations over and over for next years

Answer 32

suppose if March 1 is Sunday (0),
the June 1 will be : 3+2+3 = 8 = 1 = Monday

Answer 33

yeah

Answer 34

suppose if March 13* is Sunday (0), the June 13* will be : 3+2+3 = 8 = 1 = Monday

Answer 35

by same process

Answer 36

can u see a way to rearrange all this in nice matrix usable form

Answer 37

yes looks it works in general
I think if we find the day of March1, it will be simple to work the months in which 13th will fall on friday

Answer 38

Oh never thought about matrices, let me think a bit..

Answer 39

0 1 2 3 4 5 6 7
sun - sat
--------------------------------
Rems
3 0 3 2 3 2 3 3 2 3 2 3

Answer 40

i see why you think matrices will show up xD

Answer 41

Okay lets write out 12 equations

Answer 42

lets add this in too umm yearly shifts =
sum (3 0 3 2 3 2 3 3 2 3 2 3) mod 7

Answer 43

lets just ignore leapyears for now lol

Answer 44

but if u wanna account for leap years we repeat this same process except we take 48 month pattern

Answer 45

365 = 1 (mod 7)
366 = 2 (mod 7)

Answer 46

ya

Answer 47

so a non leap year advances by 1 week day
if this year starts with Sunday, then next year will start with Monday ?

Answer 48

yeah

Answer 49

that looks interesting

Answer 50

lets try to get it in this form
A B = C

Let A be the transformation matrix
Let B be in the input vector taking 2 parameters, one for the year difference from now and the day in the year

For example B=<3,200> means 3rd year from now and 200th day

Answer 51

and we shud probably hold Now in some Vector

Answer 52

or forget now as a vector lets just take it always relative to jan 1st of 2015

Answer 53

and C has to be just 1 output for the day thats good enuff for now

Answer 54

if C=0 then sunday C=1=monday... and so on