Andy's Birthdate

[rocdocmac]

Earlier today (whilst attending his birthday party) I asked Andy his age, but he said that I can figure that out easily by myself! All I had to do was to add four numbers together.

The first of these four numbers is the last digit in the figure obtained when 2 is raised to the power of 667788 (2⁶⁶⁷⁷⁸⁸). Similarly, I had to find the last digit in the evaluation of 3⁵⁵⁶⁶⁷⁷, 7⁴⁴⁵⁵⁶⁶, and 8³³⁴⁴⁵⁵ to complete the sum.

If today is the 12^th of March 2020, when was Andy born?

Edited March 12, 2020 by rocdocmac
Wording change

[CaptainEd]

I’m pretty sure I know; the answer follows and then hidden analysis:

Andy’s birthday was 3/12/2004

analysis follows:

first number: the last digit of powers of 2 goes through the cycle (2486), with an exponent  divisible by 4 endinG in 6. The given exponent 667788 is divisible by 4, so this number is 6.

second number: the last digit of powers of 3 runs through the cycle (3971), with exponent divisible by 4 ending in 1. 556677 is 3mod4, so it ends in 7.

third number: the last digit of powers of 7 runs through cycle (7931). The exponent 445566 is divisible by 4, so this number is 1.

fourth number: last digit of powers of 8 has cycle (8426), and the exponent of 334455 is 3 mod4, so this number is 2.

His age, on his birthday 3/12/2020, was sum(6,7,1,2) = 16
so if we just count years and not distinguish leap years, he was born 3/12/2004.

[rocdocmac]

Spoiler

You need to revise!

Spoiler

Incorrect answer (50 % of digits correct).

 

 

 

[CaptainEd]

How embarrassing! I see your point, Rocdocmac. Here’s the new improved answer:

first number: The given exponent 667788 is divisible by 4, so this number is 6.
second number: 556677 is 3mod4, so it ends in 7.

(Improved) Third number: The exponent 445566 is 2mod4, so this number is 9

(improved) fourth number: the exponent of 334455 is 1mod4, so this number is 8.

Total = 30

birthday mar 12, 1990

[rocdocmac]

Spoiler

1 up, 1 down: 50 % again! (still wrong age)

 

[CaptainEd]

Thank you Rocdocmac. Once I’m done with this, I’m going to take a high level math class on how to divide by 4.

 

 

Birthday 3/12/2000

 

Analysis follows:

 

 

first number: the last digit of powers of 2 goes through the cycle (2486), with an exponent  divisible by 4 ending in 6. The given exponent 667788 is divisible by 4, so this number is 6. 

second number: the last digit of powers of 3 runs through the cycle (3971), with exponent divisible by 4 ending in 1. 556677 is 1mod4 so it ends in 3.

third number: the last digit of powers of 7 runs through cycle (7931). The exponent 445566 is 2mod4 so this number is 9.

fourth number: last digit of powers of 8 has cycle (8426), and the exponent of 334455 is 3mod4, so this number is 2

So age = 6 + 3 + 9 + 2 = 20

 

I hope that’s that!

Edited March 19, 2020 by CaptainEd

[rocdocmac]

YAY!

On 3/19/2020 at 7:45 PM, CaptainEd said:

second number: the last digit of powers of 3 runs through the cycle (3971), with exponent divisible by 4 ending in 1. 556677 is 1mod4 so it ends in 3.

second number: the last digit of powers of 3 runs through the cycle (3971), with exponent divisible by 4 ending in 1. 556677 is 1mod4 so it ends in 3.