| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Picture yourself in an empty room with two doors. One of the doors
leads to freedom, while the other one leads to another empty room
with four doors. In the room with four doors, one of the doors leads
to freedom, while the other three doors lead to another empty room
with eight doors. Thereafter follows a sequence of rooms in which
the number of doors are doubled every time, but only one door in
each room leads to freedom. Thus, in the tenth room, there would be
one thousand and twenty-four doors of which just one leads to
freedom.
Furthermore, when you open a door in a room, the other doors in that
room become locked forever.
Ignoring the physical problems involved, what is the probability of
your never getting out of this House of Infinities?
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1924.1 | WRKSYS::ROTH | Geometry is the real life! | Thu Dec 22 1994 12:04 | 7 | |
Are you going to be particular and ask for a closed form? Consider the sum where p takes the value 1/2 s = 1 - p - p^2 + p^5 + p^7 - p^12 - p^15 + p^22 + p^26 - p^35 - p^40 + ... - Jim | |||||
| 1924.2 | SSAG::LARY | Laughter & hope & a sock in the eye | Thu Dec 22 1994 14:09 | 5 | |
Another way of expressing this sum is: 1 1 1 1 --- - ----- + -------- - ----------- ... = 0.288788.... 1*3 1*3*7 1*3*7*15 1*3*7*15*31 | |||||
| 1924.3 | STKAI1::T_ANDERSSON | The Tank Engine | Fri Dec 30 1994 09:10 | 7 | |
All right, that was easy... Now for something trickier(?): Suppose that you are equipped with a device that allows you to remove all doors in a room except two, one of which is the door to freedom. Unfortunately, this device can be used just once, and then vanishes. When would you use this device? Is there a paradox involved? | |||||