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More ways to get Braingle...

Sum-day Soon

Math brain teasers require computations to solve.

 

Puzzle ID:#32809
Fun:*** (3)
Difficulty:*** (2.25)
Category:Math
Submitted By:hottiexo247****

 

 

 



Some people believe that January 1, 2000 is the first day of the 21st century. Other people believe that the honor belongs to January 1, 2001. But everyone should agree that January 1, 2002 is the first "sum-day" of the new century- when you write out that date in standard notation, it becomes 01/01/02, and 1+1=2. More generally, a sum-day is a date in which the day and month add up to the year. With that in mind:

A) What is the last sum-day of the 21st century?

B) How many sum-days are there in the 21st century?

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Comments

sayaah92*us*
Sep 03, 2006

took me a while, but I got it!!!! Very cool.
(user deleted)
Sep 12, 2006

Isnt there more than one per year on some years?

3/2/05
2/3/05
1/4/05
5/1/05....
(user deleted)
Sep 12, 2006

haha, nevermind, I figured it out. oops
teasermaster**
Oct 13, 2006

Very good, but there are actually 366
(including 2/29/31)
memtal
May 28, 2007

IF you go by the logic that 2043 is the last sum year. then shouldn't there are no sum years after 43 and uptil 43 there are 45+24+1= 70 sum years.

I do see your logic about the leap years and and that it should be 365 days according to this logic.


However it is in conflict with the
previously mentioned 70 years. I am confused
javaguru*us*
Jan 02, 2009

Congrats! Very nice logical teaser.
plokolplokph
Jan 17, 2009

very nice teaser...
and to everyone confused, THERE IS NOTHING WRONG WITH THIS TEASER.
@memtal, i don't get your first statement...
doeheadAus*
Jan 17, 2009

There are too many answers to this question for it to have any logic.
bradon182001*us*
Jan 17, 2009

Good thought provoking teaser. Gave me reason to do some thinking this morning. Thanks for posting.
talanpoeAus*
Jan 17, 2009

Great Teaser, and absolutely correct! Thanks for waking my braincells up this morning.
BigTexas27
Jan 17, 2009

actual answer 355. Starting in 2002 there is only one day - 1/1/02. Whatever formula used does not seem to take into account the all months do not end with the same number.

There are two in 2003.
This number increases by one each year until 2013 where there are 12 per year until 2032.

Beginning in 2033 it drops by two to 10 because February ends with 28 days.
Every two tears beginning in 2033 the total drops by 2 until 2039 where there are five days
Then it continues dropping by two until 2042 where there is one day and then the last day 12/31/43.
So the breakdown goes like this :

2002 - 1
2003 - 2
2004 - 3
2005 - 4
2006 - 5
2007 - 6
2008 - 7
2009 - 8
2010 - 9
2011 - 10
2012 - 11
2013 - 12 until 2032(19yrs) = 228
2033 - 10
2034 - 10
2035 - 8
2036 - 8
2037 - 6
2038 - 6
2039 - 5
2040 - 3
2041 - 3
2042 - 1
2043 - 1
I figured this out by hand, yes I was bored this morning.
sharoc
Jan 17, 2009

The first part was very easy, the second part tricked me because I forgot to put on my thinking cap!
mepapaAus*
Jan 17, 2009

OW!OW!OW!... that hurts my head
auntiesisAus*
Jan 17, 2009

Too long and drawn out for me. I gave up after I got a few.
kauphi1976Aus*
Jan 17, 2009

1 and 2 were easy but ended doing 2 by the hard way . When i looked at the soln it was very elegant ! like duhhh..
FatHeadAus*
Jan 17, 2009

Too easy, once I saw the easy way to do it. I mean, it would be a pointless teaser to ask something like "add up the first 1000 primes", when there's no easy way to do that like there is the first 1000 numbers, squares, triangles, Fibanoccis, etc.
iforgotbraingleAus*
Jan 17, 2009

I tried the millennium instead of century so I failed
here2A*
Jan 17, 2009

the method for part b is much easier than that way I went at it. I did more like BigTexas27, above. I think he had too many days in 2032 and 2031. Also, got a different total. I got the 365 the hard way.

Very nice puzzle. I enjoyed it. Thanks.
UptheHillA*
Jan 17, 2009

I'm with him, pass the asprin!!!
precious1026Aus*
Jan 17, 2009

To Sum this all up, funny with the possibility of some small sum of logic, but not much Loved the Teaser, and the Loved the summation the most.
dogg6pound9Aus*
Jan 17, 2009

HUH?!?!?... i am sure this is a good teaser, but what would make me want to sit down and figure this out???... i have been out of school for 15 years now, and what you guys are learning in school is great, dont get me wrong, but when you never learned a simple equation to figure this out, it it kinda hard to understand what you are talking about... in other words, i am completely lost
zaya*
Jan 20, 2009

Great teaser, thanks
PaladinAus*
Mar 13, 2009

By definition, the only "variable" in figuring out a sum-day is the year. Given any month/day combination, the sum-day occurs during the year which is the sum of the given month and day. By this logic, at most there can be 365 sum-days.

To figure out how many there are, just subtract any month/day combinations that don't have a given year to make a sum-day. Since there are none, 365-0 = 365.

To be more explicit, the following is a list of all the sum-days in the 21st century (gotta love Excel!):

Date Month Day sum-day
Jan-01 1 1 2002
Jan-02 1 2 2003
Jan-03 1 3 2004
Jan-04 1 4 2005
Jan-05 1 5 2006
Jan-06 1 6 2007
Jan-07 1 7 2008
Jan-08 1 8 2009
Jan-09 1 9 2010
Jan-10 1 10 2011
Jan-11 1 11 2012
Jan-12 1 12 2013
Jan-13 1 13 2014
Jan-14 1 14 2015
Jan-15 1 15 2016
Jan-16 1 16 2017
Jan-17 1 17 2018
Jan-18 1 18 2019
Jan-19 1 19 2020
Jan-20 1 20 2021
Jan-21 1 21 2022
Jan-22 1 22 2023
Jan-23 1 23 2024
Jan-24 1 24 2025
Jan-25 1 25 2026
Jan-26 1 26 2027
Jan-27 1 27 2028
Jan-28 1 28 2029
Jan-29 1 29 2030
Jan-30 1 30 2031
Jan-31 1 31 2032
Feb-01 2 1 2003
Feb-02 2 2 2004
Feb-03 2 3 2005
Feb-04 2 4 2006
Feb-05 2 5 2007
Feb-06 2 6 2008
Feb-07 2 7 2009
Feb-08 2 8 2010
Feb-09 2 9 2011
Feb-10 2 10 2012
Feb-11 2 11 2013
Feb-12 2 12 2014
Feb-13 2 13 2015
Feb-14 2 14 2016
Feb-15 2 15 2017
Feb-16 2 16 2018
Feb-17 2 17 2019
Feb-18 2 18 2020
Feb-19 2 19 2021
Feb-20 2 20 2022
Feb-21 2 21 2023
Feb-22 2 22 2024
Feb-23 2 23 2025
Feb-24 2 24 2026
Feb-25 2 25 2027
Feb-26 2 26 2028
Feb-27 2 27 2029
Feb-28 2 28 2030
Feb-29 2 29 2031
Mar-01 3 1 2004
Mar-02 3 2 2005
Mar-03 3 3 2006
Mar-04 3 4 2007
Mar-05 3 5 2008
Mar-06 3 6 2009
... ... ... ...
Sep-28 9 28 2037
Sep-29 9 29 2038
Sep-30 9 30 2039
Oct-01 10 1 2011
Oct-02 10 2 2012
Oct-03 10 3 2013
Oct-04 10 4 2014
Oct-05 10 5 2015
Oct-06 10 6 2016
Oct-07 10 7 2017
Oct-08 10 8 2018
Oct-09 10 9 2019
Oct-10 10 10 2020
Oct-11 10 11 2021
Oct-12 10 12 2022
Oct-13 10 13 2023
Oct-14 10 14 2024
Oct-15 10 15 2025
Oct-16 10 16 2026
Oct-17 10 17 2027
Oct-18 10 18 2028
Oct-19 10 19 2029
Oct-20 10 20 2030
Oct-21 10 21 2031
Oct-22 10 22 2032
Oct-23 10 23 2033
Oct-24 10 24 2034
Oct-25 10 25 2035
Oct-26 10 26 2036
Oct-27 10 27 2037
Oct-28 10 28 2038
Oct-29 10 29 2039
Oct-30 10 30 2040
Oct-31 10 31 2041
Nov-01 11 1 2012
Nov-02 11 2 2013
Nov-03 11 3 2014
Nov-04 11 4 2015
Nov-05 11 5 2016
Nov-06 11 6 2017
Nov-07 11 7 2018
Nov-08 11 8 2019
Nov-09 11 9 2020
Nov-10 11 10 2021
Nov-11 11 11 2022
Nov-12 11 12 2023
Nov-13 11 13 2024
Nov-14 11 14 2025
Nov-15 11 15 2026
Nov-16 11 16 2027
Nov-17 11 17 2028
Nov-18 11 18 2029
Nov-19 11 19 2030
Nov-20 11 20 2031
Nov-21 11 21 2032
Nov-22 11 22 2033
Nov-23 11 23 2034
Nov-24 11 24 2035
Nov-25 11 25 2036
Nov-26 11 26 2037
Nov-27 11 27 2038
Nov-28 11 28 2039
Nov-29 11 29 2040
Nov-30 11 30 2041
Dec-01 12 1 2013
Dec-02 12 2 2014
Dec-03 12 3 2015
Dec-04 12 4 2016
Dec-05 12 5 2017
Dec-06 12 6 2018
Dec-07 12 7 2019
Dec-08 12 8 2020
Dec-09 12 9 2021
Dec-10 12 10 2022
Dec-11 12 11 2023
Dec-12 12 12 2024
Dec-13 12 13 2025
Dec-14 12 14 2026
Dec-15 12 15 2027
Dec-16 12 16 2028
Dec-17 12 17 2029
Dec-18 12 18 2030
Dec-19 12 19 2031
Dec-20 12 20 2032
Dec-21 12 21 2033
Dec-22 12 22 2034
Dec-23 12 23 2035
Dec-24 12 24 2036
Dec-25 12 25 2037
Dec-26 12 26 2038
Dec-27 12 27 2039
Dec-28 12 28 2040
Dec-29 12 29 2041
Dec-30 12 30 2042
Dec-31 12 31 2043

The total is 366, but 02/29/2031 is not a valid date, so the total is 365 (as stated in the answer)

Well done!
Awkward
Apr 15, 2009

Damit I did it out by hand and got 364. Must have dropped 1 somewhere along the line.
Great teaser though
dalfamnestAnz*
Feb 01, 2010

Great thinking, Paladin! I was on a tack like that, but got interrupted and checked the answer ... as so often happens, now I wish I'd given it more time.

That makes this a top teaser!
gaylewolfAus*
Jan 17, 2012

Fascinating teaser - I admire people who figured this one out - especially those who didn't use a calculator!
However it's not my thing and I was only half awake when I tried it.
Give me a good old word puzzle.
PS Babe, how did I beat you here today!
HABS2933Aca*
Jan 17, 2012

Not sure why we were given a calculator to figure this out. I did it using a pen and paper and had no trouble. Of course I went to school in the dark ages where until we reached the upper high school grades and more advanced maths like trig and calculus using a calculator was considered cheating and being caught with one was an auto-fail. It was a great teaser that for the people who put wanted to put in the time to figue it out, it was very doable.
HABS2933Aca*
Jan 17, 2012

Not sure why we were given a calculator to figure this out. I did it using a pen and paper and had no trouble. Of course I went to school in the dark ages where until we reached the upper high school grades and more advanced maths like trig and calculus using a calculator was considered cheating and being caught with one was an auto-fail. It was a great teaser that for the people who put wanted to put in the time to figue it out, it was very doable.
TallTimberAus*
Jan 17, 2012

Well done. Pencil and paper for me as well. lol
wordmama*
Jan 17, 2012

I'm with HABS on the calculator issue vis a vis school!! As for this teaser, I love math and would love to have figured this out but have a FEW other things to accomplish today! (part A of course was easy!)
Mandy7us*
Jan 17, 2012

Interesting. I never knew this kind of stuff. Thanks for opening my eyes to some more things in the world!



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