my birthday's in july each year, the same date every time. when my birthday is tomorrow, the day before yesterday is prime. two weeks after my birthday the date would always be a very small square number added to a power of three. if my birthday falls on sunday the next saturday furthermore has a date with six factors and is a multiple of four. there are only two possibilities the verses above create. choose the smaller of the two to find my birthday date.
Most difficult question, challenge: who can solve this problem
Answers
Happy birthday !!!!!!
Given : birthday's in july each year, the same date every time.
To Find : find birthday date.
Solution:
when my birthday is tomorrow, the day before yesterday is prime
3 Days before birthday is prime
Prime numbers 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31
Birth day can be on
5 , 6 , 8 , 10 , 14 , 16 , 20 , 22 , 26 , 2 , 3 ( ∵ june has 30 day )
writing in order
2 , 3 , 5 , 6 , 8 , 10 , 14 , 16 , 20 , 22 , 26
two weeks after my birthday the date would always be a very small square number added to a power of three.
very small square number is 1
3⁰+ 1 = 2 , 3¹ + 1= 4 , 3² + 1 = 10 , 3³ + 1 = 28
subtracting 14 to get birth date ( July has 31 Days)
19 , 21 , 27 and 14
my birthday falls on sunday the next saturday furthermore has a date with six factors and is a multiple of four.
next Saturday would be after 6 days
12 = 1 , 2 , 3 , 4 , 6 , 12
20 = 1 , 2 , 4 , 5 , 10 , 20
28 = 1 , 2 , 4 , 7 , 14 , 28
Hence birthday can fall on
6 , 14 or 22
Common in all is 14
Hence Date of Birth is 14
11 is prime
two weeks after my birthday 28 , 3³ + 1 = 28
next Saturday on 20
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