69105 (number)
| ||||
|---|---|---|---|---|
| Cardinal | sixty-nine thousand one hundred five | |||
| Ordinal |
69105th (sixty-nine thousand one hundred and fifth) | |||
| Factorization | 3 × 5 × 17 × 271 | |||
| Roman numeral | LXVMMMMCV | |||
| Binary | 100001101111100012 | |||
| Ternary | 101112101103 | |||
| Quaternary | 1003133014 | |||
| Quinary | 42024105 | |||
| Senary | 12515336 | |||
| Octal | 2067618 | |||
| Duodecimal | 33BA912 | |||
| Hexadecimal | 10DF116 | |||
| Vigesimal | 8CF520 | |||
| Base 36 | 1HBL36 | |||
The number 69,105 was used as an in-joke at the computer game manufacturer Infocom. It has occasionally appeared in later computer games as a tribute to Infocom.
Significance of the number
The number 69,105 makes a number of appearances in Infocom games. Nick Montfort, in his book Twisty Little Passages (ISBN 0-262-13436-5), suggests that the number was chosen not only because 69 is the common name of a sexual position, but also because in its written form 69,105 falls naturally into two parts with an unusual relationship:
- 69 in hexadecimal is 105 in decimal
- 69 in decimal is 105 in octal
This property was pointed out in a version of the Jargon File dating back at least to 1982. Commenting on the ("Exclusive to MIT-AI") usage of 69 as a generic "large quantity", Guy L. Steele said, "I don't know whether its origins are related to the obscene interpretation, but I do know that 69 decimal = 105 octal, and 69 hexadecimal = 105 decimal, which is a nice property."[1]
The same natural relationship applies to 1,001; 2,002; 3,003; 4,004; 5,005; 6,006; 7,007; 64,100; 65,101; 66,102; 67,103; and 68,104. However, 69,105 is the highest number with this property with fewer than six digits.
In mathematics
69105 is the third 23036-gonal number and the fifth 6912-gonal number. It is also the 17th 510-gonal and the 15th 660-gonal number.
As of September 2011, the only OEIS reference to 69105 is (sequence A097830 in OEIS), "Partial sums of Chebyshev sequence S(n, 16)", with 69105 corresponding to n = 4.
Appearances
Appearances in Infocom games
Beyond Zork
There are 69,105 Christmas tree monsters.
Bureaucracy
The sample transcript includes a ticket with the description:
Ticket number 69105. Seat 25F. Acme Building Auditorium.
Running the adventure game cartridge causes the Boysenberry computer to crash almost immediately, with the message:
INTERNAL ERROR 69105.....
Deadline
The serial number on the pharmacy label on the tablets is 69105.
Leather Goddesses of Phobos
There are 69,105 leaves in the sack found in Cleveland, Ohio.
Trinity
There are 69,105 leaves in the book in the cottage.
Wishbringer
At the lake edge, a "count leaves" gives:
A quick count turns up exactly 69,105 leaves.
The Witness
The gun receipt used as a bookmark in the mystery book is number 69105.
Zork I
Probably its most famous appearance:
On the ground is a pile of leaves.
>count leaves
There are 69,105 leaves here.
Zork Zero
This zoo, with 69,105 cages, is easily the largest in Quendor.
Zork: The Undiscovered Underground
Entering the Theater from the Cultural Complex:
Built to the precise specifications of Lord Dimwit Flathead, its excessive structure holds 69,105 seats, …
Appearances in later games
In Advanced Xoru, after you drink a potion, you drop it to the floor "shattering into 69,105 shards of glass".
In Adam Cadre's game I-0:
>open trunk
You open the trunk, revealing your laundry.
>examine laundry
There are 69,105 pieces of laundry here.
In the NES version of Ultima: Quest of the Avatar, one of the mages claims he's working on a book that has 69,105 pages so far.
In the Kingdom of Loathing strange leaflet game-within-game, a parody of classic text adventures, the player can count leaves and find 69,105 of them.
In TempusMUD, the throne of the Grand Mistress of Magic is made of 69,105 emeralds.[2]