Thursday Birthday
Tom was born on a Thursday in either 2014, 2015, 2016, or 2017. What is the oldest age Tom can turn on his next Thursday birthday?
Hint : Consider the remainder when the number of days in a year (365) is divided by the number of days in a week (7). But don't forget about leap years!
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5 solutions
Maybe it is worth noting that February 29, 2016 was Monday. If someone is born in Monday, February 29, 2016, he will have his next Monday birthday on Monday, February 29, 2044, at the age of 28. (leap to leap year is +5, so you have to wait a full cicle of 7 leap years for the same day to apper)
My birthday is November 27th. Occasionally it falls on Thanksgiving. I had already figured this out a long time ago lol. Great question though!
Nice problem. The 1 to 5 correct to incorrect ratio is really bad since the hint gives the problem away. You should have just reminded us to count for leap years Stephen Mellor!
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I can't edit the problem now, as this hint was added in when it became a problem of the week. I agree that hinting about leap years is useful, and maybe not so much about the remainder part.
I guess the problem of this one is the way the question was writen... sorry. Maybe is my English, but I simply didn’t understand the question
Could u pls explain why is Fri (1), Sun (2), Mon (3), Tue (4), Wed (5), Fri (6), Sat (7), Sun (8), Mon (9), Wed (10), Thu (11)???
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The logic basically works by saying that every year, you have exactly 52 weeks and 1 day left over. In a normal year progression, that would mean the days are offset by 1 every year. But during a leap year, you add an extra day which would mean you should go forward by 1 extra day alongside the two. So if you are born two years before a leap year, it would mean the progression would be thursday(day you were born) - friday - sunday...
the numbers in brackets are the ages of Tom when his Birthday is on that day of the week
It seems to me that whilst you have the correct answer, because you are correct that there are 3 leaps you have not quite got the days correct. Because there are THREE consecutive days and then the leap (NOT 4 CONSECUTIVE DAYS!). So it should be Fri, Sat, LEAP to Mon, Tues, Wed, LEAP to Fri (in order to avoid the birthday falling on Thursday. Then Sat, Sun, LEAP to Mon, Tues, Wed, THURS which is the 11th birthday. Regards, David
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January 8, 2015 -> is a Thursday
January 8, 2016 -> is a Friday
January 8, 2017 -> is a Sunday
Jaunary 8, 2018 -> is a Monday
Jaunary 8, 2019 -> is a Tuesday
Jaunary 8, 2020 -> is a Wednesday
Jaunary 8, 2021 -> is a Friday
Jaunary 8, 2022 -> is a Saturday
Jaunary 8, 2023 -> is a Sunday
Jaunary 8, 2024 -> is a Monday
Jaunary 8, 2025 -> is a Wednesday
Janunary 8, 2026 -> is a Thursday
It is 4 consecutive days because you also have a birthday in the leap years.
Imagine it this way: there is exactly 4 years between February 29th and the next February 29th. You will be guaranteed to have 4 birthdays in this gap, and it is only on the 29th of February that the leaps happen.
Every year, the birthday will be one weekday later. But in leap years, it is two days later.
For every four years older, the birthday will be five weekdays later.
Therefore, we have
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birthday 0 on Thursday
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birthday 4 on Tuesday
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birthday 8 on Sunday
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birthday 12 on Friday
and so on. The first Thursday could be between birthdays 4 and 8; the only way to skip it, is if birthday 5 is on Wednesday and birthday 6 is on Friday. However, in that case we have four years later birthday 9 on Monday, birthday 10 on Wednesday, and birthday 11 on Thursday.
Note
The really correct answer would be 28. This happens if Tom is born on February 29, 2016. Check it out!
Tom is born on a Thursday, and 29/02/16 was a Monday
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True, that. Too bad when facts get in the way of theory!
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I think that this is why, when adapted for a problem of the week, the years 2014-2017 were specified!
If he was born on Feb 29 he only gets a birthday every 4 years :)
The "really correct answer" is 11 if he was born on 6th march 2014
29-Feb-2016 was on Monday. Not relevant with this question
Very important that the question is asking the "oldest". Consider that 2020 is a leap year which if he was born on a Thursday in 2014 (before Feb 29), his 2020 birthday will be on Friday because of the leap year +1 day. In calculation the final answer turns out to be 2025- 2014= 11. Pretty scary the 20% correction rate
actually, If tom was born 2015 prior to the end of February he also turns 11 on Thursday 2026...not just 2014 after february
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I think Terrence means to say "after Feb 29" not "before Feb 29" for 2014. A person born in January or February of 2014 will celebrate his 6th birthday on a Thursday in 2020. Because only one leap day would be in between.
I didn't really get what the question was asking. What's a leap year? I would rate this problem a 9 because it was a bit confusing.
Remainder sequence (Day difference of consecutive years divided by 7 + previous remainder):
2(ly), 3, 4, 5, 0(ly) :Age - 5yr
1, 3(ly), 4, 5, 6, 1(ly), 2, 3, 4, 6(ly), 0 :Age - 11yr
1, 2, 4(ly), 5, 6, 0 :Age - 6yr
1, 2, 3, 5(ly), 6, 0 :Age - 6yr
(ly indicates a leap year)
2016 was a leap year. On 29th feb it was monday that year. Suppose that it would have been a thursday on 29th. Then the ans would have been 28 years. If you do the math you would find that on 29th feb 2020 it would be Tuesday,sunday in 2024 ... and thurday again in 2044. So it would be 28 years.
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That's why it's framed properly; the birthday is not on 29th Feb given the last part of question. Thanks for your information :)
Just to make this concrete: If Tom is born on Thursday, January 1, 2015, then his birthdays are:
- Thursday, January 1, 2015 (age 0)
- Friday, January 1, 2016 (age 1)
- Sunday, January 1, 2017 (age 2) -- skipped a day because 2016 was a leap year.
- Monday, January 1, 2018 (age 3)
- Tuesday, January 1, 2019 (age 4)
- Wednesday, January 1, 2020 (age 5)
- Friday, January 1, 2021 (age 6) -- skipped a day because 2020 was a leap year.
- Saturday, January 1, 2022 (age 7)
- Sunday, January 1, 2023 (age 8)
- Monday, January 1, 2024 (age 9)
- Wednesday, January 1, 2025 (age 10) -- skipped a day because 2024 was a leap year.
- Thursday, January 1, 2026 (age 11)
Note that this is obviously not the best way to find the solution, but it confirms that we have the right one.
3 6 5 / 7 has a remainder of 1, so the excess day on a "regular" year will advance the day of the week by 1.
3 6 6 / 7 has a remainder of 2, so a "leap" year will advance the day of the week by 2.
They go in the pattern regular-regular-regular-leap-regular-regular-regular-leap-etc.
Now we need a sequence that avoids Thursday as long as possible. It's clear we can stall by "leaping" over it at least once, that is, we'll have
Now we can fill in forwards and backwards; there will be 3 regular years after the leap and before the leap.
Now "leap" before and after:
Extending this any farther in either direction will result in a Thursday. Counting (and including the fact the story says the last birthday will be a Thursday):
Thu (0, is born), Fri (1), Sun (2), Mon (3), Tue (4), Wed (5), Fri (6), Sat (7), Sun (8), Mon (9), Wed (10), Thu (11)
So Tom has turned 11 years old.
If you want to see this on a real calendar, January 8, 2015 to January 8, 2026 will do the trick.