# VERY LARGE NUMBER.

cosmic voice
Posers and Puzzles 12 Nov '04 07:58
1. 12 Nov '04 07:58
FIND THE LAST 10 DIGITS OF 9^(9^(9^9))
2. TheMaster37
Kupikupopo!
12 Nov '04 10:45
All I can tell is that it ends in a 9
3. genius
Wayward Soul
12 Nov '04 11:084 edits
i was bored so i attempted to find patterns with 9^whatnot...

col 10=1,9,1,9 etc
col 9=8,2,6,4,4,6,2,8,0,0 then repeats

so if it's 9^an odd number, it'll end in 9.
9^a even number, it'll end in 1.
divide the (power-1) by 10, and if the remainders 1 then the second last digit of 9^ that number shall be a 8, if it's 2 it'll be a 2 etc (there are 10 numbers that repeat over)

so, 9^(9^(9^9)).

9^(9^9) is odd, so the last digit shall be 9. and 9^9 is 387420489, which is odd, so the second last digit of 9^(9^9) shall be 2. it'll end in 29. thus 9^(9^(9^9)) shall end in 89.

i am bored. if you see a flaw, tell me. but from what i can see, that is correct...so, who's willing to find out the next 8 digits? ðŸ˜‰

coloum 8 goes (if we sub 1 for odd and 2 for even) 1122112222 and repeats...

also-this is just using 9^1 to 25...
4. Palynka
Upward Spiral
12 Nov '04 12:27
Originally posted by cosmic voice
FIND THE LAST 10 DIGITS OF 9^(9^(9^9))
0123456789 ?
5. squaccerman
The 17th coming
12 Nov '04 13:01
&quot;so if it's 9^an odd number, it'll end in 9.
9^a even number, it'll end in 1.&quot;

Surely if it ends in one it is not an even number.
6. genius
Wayward Soul
12 Nov '04 13:37
Originally posted by squaccerman
"so if it's 9^an odd number, it'll end in 9.
9^a even number, it'll end in 1."

Surely if it ends in one it is not an even number.
to the power an even number, e.g 9^124235432 shall end in 1, but 9^124235433 shall end in 9
7. 12 Nov '04 15:271 edit
Originally posted by Palynka
0123456789 ?
No that's not correct. Only the last two digits are correct. The process of finding the answer involves modular mathematics.
8. 12 Nov '04 16:40
Originally posted by cosmic voice
FIND THE LAST 10 DIGITS OF 9^(9^(9^9))
3111098189

raise 9 to the power of a number of form kx10^n:
- (n=0): The units digit cycles 1,9 and repeats
- (n=1): The tens digit cycles every 10 (01,01,81,21,61,41,41,61,21,81)
- (n&gt;2): Subsequent digits cycle according to their digit.
kx10^n (k=0,1,2,...,9; n=2,3,...,9) has last (n+1) digits of
jx10^n+1 where j=0,4,8,2,6,0,4,8,2,6 for k = 0,1,2,3,4,5,6,7,8,9

9^9 is 387420489
9^9^9 has the same last 10 digits as 200000001.20000001.8000001.1.400001.1.601.21.9 which has the same last 10 digits as 2835673589 (obviously when you multiply you can just disgard any digits after the last 10).

Repeat the process and you get the answer.
9. 12 Nov '04 18:191 edit
What are the last ten digits of (((((((9^9)^9)^9)^9)^9)^9)^9)^9?
10. 13 Nov '04 00:01
Originally posted by Glenton
3111098189

raise 9 to the power of a number of form kx10^n:
- (n=0): The units digit cycles 1,9 and repeats
- (n=1): The tens digit cycles every 10 (01,01,81,21,61,41,41,61,21,81)
- (n>2): Subsequent digits cycle according to their digit.
kx10^n (k=0,1,2,...,9; n=2,3,...,9) has last (n+1) digits of
jx10^n+1 where j=0,4,8,2,6,0,4,8,2,6 for k = 0,1, ...[text shortened]... ou can just disgard any digits after the last 10).

Repeat the process and you get the answer.
Agree
11. 16 Nov '04 14:17
Originally posted by THUDandBLUNDER
What are the last ten digits of (((((((9^9)^9)^9)^9)^9)^9)^9)^9?
This number (given by you in your quoted post) is not very large number .....In fact it is miniscule when comparedto the number given in the puzzle.
12. 16 Nov '04 20:402 edits
4256697609

ðŸ˜´
13. 17 Nov '04 17:35
Originally posted by Gronk
4256697609

ðŸ˜´
NOPE...that is wide off the mark. you cant write all the digits of the number even if you have a scroll as wide as the earth's diameter and if
each digit took just half a centimetre width.
14. 21 Nov '04 12:161 edit
Originally posted by cosmic voice
NOPE...that is wide off the mark. you cant write all the digits of the number even if you have a scroll as wide as the earth's diameter and if
each digit took just half a centimetre width.
Whaoh......? REALLY ?
15. Acolyte