A friend of mine has an interesting birthday.

If you shorten the date month and year and use UK date format, it reads the year in full, his birthday falls on a Friday.

When he is as old as the year of his birth (last two digits of the year), his birthday will also be a Friday, lets call this the Magic day.

He observed that there could be many dates similar to his birthday, however he noted that for one such date in the past, his birthday is the Magic day.

Can you find my friends' birthday if he is still alive?

  • 4
    $\begingroup$ You might want to clarify what "UK date format" is for those who don't live in the UK. $\endgroup$ – Moyli Nov 1 '14 at 11:29
  • $\begingroup$ I think this is a duplicate but I can't find it. I remember it though! $\endgroup$ – warspyking Nov 1 '14 at 11:33
  • $\begingroup$ Oh come on, this is made up by me... can never be a duplicate $\endgroup$ – skv Nov 1 '14 at 11:34
  • $\begingroup$ possible duplicate of Odd birthdate surprise $\endgroup$ – warspyking Nov 1 '14 at 11:38
  • 4
    $\begingroup$ If you think this question is a duplicate of that... may lord bless you $\endgroup$ – skv Nov 1 '14 at 11:53

If I got this right the "magic day" would be the day/month/year that his birthday falls on, in which his age matches up with the last 2 dates of the year he was born?

Well, here's one possible solution. The birth date fell on:


The birthday ("magic day") was:


If the above is his DOB then HIS magic day would be:


Otherwise, we'd need to know his age.


Obviously the day and month had to be the same in both dates. We should try 1/9 first, it's the most logical assumption as it's closest to us. Meaning it's September the 1st. Going through the trial and error method, we eventually find 1/9/39. We then check 1/9/78 because obviously the year has to be doubled for the person's age to match the last 2 digits. Low and behold, it's on a Friday. Then of course to find his magic day we go ahead of 1978 by, obviously, 78, to get 2056!

He is in fact still alive.

It took me a while to answer this, because it seemed to me as if the question wanted the DOB and the magic day, I didn't get the part about HIS magic day and the other person's magic day being his DOB.

Alternative Solution:

If you go back farther than 1939 you can also find DOB: 1911 and Magic Day: 1922 making his birthday/magic day: 1944

But this won't fit the question as the question states his birthday on his magic day "will be" indicating that this Magic day is in future

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  • $\begingroup$ I think the understanding is correct, but the question is not what you have answered $\endgroup$ – skv Nov 2 '14 at 2:03
  • $\begingroup$ How did I not answer the question? I provided both his date of birth, and his birthday (the "magic day"). In fact I didn't even need to give you his DOB as all you ask for is the birthday, and I quite "Can you find my friends' birthday if he is still alive" $\endgroup$ – warspyking Nov 2 '14 at 9:14
  • $\begingroup$ @skv Well? How didn't I? $\endgroup$ – warspyking Nov 2 '14 at 10:13
  • $\begingroup$ I think there is a slight misunderstanding, magic day is supposed to be the birthday that you will celebrate when you are as old as the last two digits of your year of birth. You have identified the facts, but if you modify the answer accordingly I shall accept $\endgroup$ – skv Nov 2 '14 at 10:21
  • $\begingroup$ @skv I have given you the magic day, and I gave the DOB, and I explained how I got it. What other information could I possibly be missing? $\endgroup$ – warspyking Nov 2 '14 at 10:27

September 1st 1978

His Magic day:

September 1st 2056

His birthday is magic day for

September 1st 1939


UK date representation is DDMMYYYY, puzzle shortened it so it would be DMYY. Friend could not be younger than 16 since 2/0 doesn't account for any date, so D/M has to be 1/9, hence first of Sept. Testing years going back, this date was on Friday on 95 & 89 but Since Magic day is adding a number to itself, it can't be on a odd numbered year. Next one back is 78, where 2056 has the Magic day, and dividing the number by 2 to 1939 shows us that the date 1/9/78 is indeed Magic day for 1/9/39. 1950 could have worked, but 1/9/25 was not a Friday. No other 19xx date would be relevant, since before 1950 Magic day would come out in 19xx's, but we eliminated those (Besides 78, which is our answer). Going back to 18xx years would be against the "Friend being alive" rule...

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  • $\begingroup$ You didn't explain how you got your answer, so you may not get to keep the accepted answer. You do not pick which is accepted due to speed, you pick due to quality! :D $\endgroup$ – warspyking Nov 2 '14 at 16:25
  • $\begingroup$ @warspyking, like it now? $\endgroup$ – JNF Nov 2 '14 at 16:43
  • $\begingroup$ Not exactly, I like the explanation but "Can you find my friends' birthday if he is still alive" is not a rule, it seems to imply it wants you to state if the person is dead though. $\endgroup$ – warspyking Nov 2 '14 at 17:10
  • $\begingroup$ There is one more entire set which meets all my rules (Except one subtle rule in the question) can you find that out if you are curious $\endgroup$ – skv Nov 2 '14 at 17:17

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