MathDB

Dilhan has objects of

3

types,

A

B

, and

C

, and

6

functions

f_{A,B},f_{A,C},f_{B,A},f_{B,C},f_{C,A},f_{C,B}

where

f_{X,Y}

takes in an object of type

X

and outputs an object of type

Y

. Dilhan wants to compose his

6

functions, without repeats, such that the resulting expression is well-typed, meaning an object can be taken in by the first function, and the resulting output can then be taken in by the second function, and so on. In how many orders can he compose his

6

functions, satisfying this constraint?
Proposed by Adam Bertelli

Problem Statement