A helicopter drops two trains, each on a parachute, onto a
straight infinite railway line. There is an undefined
distance between the two trains. Each faces the same
direction, and upon landing, the parachute attached to each
train falls to the ground next to the train and detaches.
Each train has a microchip that controls its motion. The
chips are identical. There is no way for the trains to know
where they are. You need to write the code in the chip to
make the trains bump into each other. Each line of code
takes a single clock cycle to execute.
You can use the following commands (and only these);
MF - moves the train forward
MB - moves the train backward
IF (P) - conditional that's satisfied if the train is next
to a parachute. There is no "then" to this IF statement.
Tis known in refined company, that choosing K things out of
N can be done in ways as many as choosing N minus K from N:
I pick K, you the remaining.
This simply states the binomial coefficient identity .
Find though a cooler bijection, where you show a knack
uncanny, of making your choices contain all K of mine.For
pedantry let K be no more than half N.
Consider a function which, for a given whole number n,
returns the number of ones required when writing out all
numbers between 0 and n. For example, f(13)=6. Notice that
f(1)=1. What is the next largest n such that f(n)=n?
Given a triangle ABC, how would you use only a compass and
straight edge to find a point P such that triangles ABP, ACP
and BCP have equal perimeters? (Assume that ABC is
constructed so that a solution does exist.)