*Adam M.
Costello*
## Puzzles

[Golden rope]
[Light bulb]
[Fuse]
[Toy soldier]

These are puzzles I've collected. I did not invent them, though I
have reworded them.

**Warning:** The hints are big hints, so resist looking
at them unless you're sure you're stumped.

There is a ceiling a hundred feet above you that extends forever, and
hanging from it side-by-side are two golden ropes, each a hundred feet
long. You have a knife, and would like to steal as much of the golden
ropes as you can. You are able to climb ropes, but not survive falls.
How much golden rope can you get away with, and how? Assume you have as
many hands as you like.

[hint]
[solution]

There are three on/off switches in one room, each controlling a
different one of the three out-of-sight light bulbs in another room.
You may manipulate the switches (only to the extent of turning them
on and off), then you must go into the room with the light bulbs and
stay there until you have determined the mapping from switches to light
bulbs. How do you do it?

[hint]
[solution]

You have two one-hour fuses (the kind that often protrude from
fireworks, not the electrical kind). Unfortunately, they don't
necessarily burn at a uniform rate; all you know is that each one takes
exactly one hour to burn completely. You can move infinitely fast. How
can you measure 45 minutes? How can you measure 40 minutes? How can
you measure 37 minutes 11 seconds?

[hint]
[solution]

A finite but unlimited number of toy soldiers will be lined up in a
row. Each one is a Moore machine (a finite state machine whose outputs
are functions of the state only, not the inputs), and is connected to
its immediate neighbors. There is a global clock signal. Each soldier
may fire its gun at most once. At an arbitrary time, the soldier on
the far left will be nudged, and some time later, all the soldiers must
fire simultaneously. You must design the state machine so that it works
no matter how many soldiers there are. In particular, if your machine
has `m` states, it must work even when there are more than
`m` soldiers. How soon after the nudge can you get them to
fire?

[hint]
[solution]