10

Part of 2016 LMT

Problems(2)

2016 LMT Individual #10

Source:

There are sixteen buildings all on the same side of a street. How many ways can we choose a nonempty subset of the buildings such that there is an odd number of buildings between each pair of buildings in the subset?
Proposed by Yiming Zheng

2016 LMT Theme #10

Source:

S=\{1,2,3,4,5,6\}.

Find the number of bijective functions

f:S\rightarrow S

for which there exist exactly

6

bijective functions

g:S\rightarrow S

f(g(x))=g(f(x))

x\in S

.
Proposed by Nathan Ramesh