2016 UNCO Math Contest II Problems/Problem 8
Problem
Tree
Each circle in this tree diagram is to be assigned a value, chosen from a set , in such a way that along every pathway down the tree, the assigned values never increase. That is, , and . (It is permissible for a value in to appear more than once.)
(a) How many ways can the tree be so numbered, using only values chosen from the set ?
(b) Generalize to the case in which . Find a formula for the number of ways the tree can be numbered.
For maximal credit, express your answer in closed form as an explicit algebraic expression in .
Solution
a) b)
See also
2016 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |