MathDB

Island Hopping Holidays offer short holidays to

64

islands, labeled Island

i, 1 \le i \le 64

. A guest chooses any Island

a

for the first night of the holiday, moves to Island

b

for the second night, and finally moves to Island

c

for the third night. Due to the limited number of boats, we must have

b \in T_a

and

c \in T_b

, where the sets

T_i

are chosen so that (a) each

T_i

is non-empty, and

i \notin T_i

, (b)

\sum^{64}_{i=1} |T_i| = 128

, where

|T_i|

is the number of elements of

T_i

. Exhibit a choice of sets

T_i

giving at least

63\cdot 64 + 6 = 4038

possible holidays. Note that c = a is allowed, and holiday choices

(a, b, c)

and

(a',b',c')

are considered distinct if

a \ne a'

b \ne b'

c \ne c'

Problem Statement