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# Andy's Birthdate

## Question

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 12th of March 2020, when was Andy born?

Edited by rocdocmac
Wording change

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• 1

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 by CaptainEd
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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.

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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

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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.

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