Suppose an ant walks along a 20 cm stick at a speed of 1 cm every second.
What is the longest
time the ant can be
on the stick before falling off?
Obviously 20 seconds if the ant starts at one end and walks to the other.
Now suppose there are several ants on the stick, starting from random positions and facing
either left or right. When two ants collide they turn around and walk back the other
way until they either collide again or fall off the stick.
Can you see through the resulting mayhem and work out what is the longest possible time
that at least one ant will remain on the stick?
Use the simulation below to help solve this problem —
see how long it takes a single ant to fall off the stick, then experiment
with more ants. Does it ever take longer for all the ants to fall?
Select the number of ants and hit Run
to reset to a random initial configuration.
Wach the Time
field to see how long the ants stay on the stick.
The other buttons toggle the available options:
- Flag — give each ant a flag that it
will exchange when colliding.
- Barriers — put barriers at the end of
the stick so the ants will not fall off.
- Alice — highlight
Alice the Ant to make it easier to
watch a single ant's motion.
- Distinct — select to give each ant its own colour.
- Sounds — turn on the sound effects.
- Elephant — elephant???