Puzzle:

Find a cycle of five 4-digit numbers such that the last 2 digits of each number are equal to the first 2 digits of the next number in the cycle. Each of the 5 numbers must be exactly one of the following types (with each of the 5 types being represented exactly once): Square, Cube, Triangular, Prime, Fibonacci. The solution is unique.

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Solution:

8117, 1728, 2850, 5041, 4181 (Prime, Cube, Triangular, Square, Fibonacci)