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Bijections

Bijections, surjections, and injections are three types of functions which associate the elements between two sets. For example, each word in this sentence can be mapped to exactly one in the last.

Level 1

         

Paula has numbered all squares of the square board above, from left to right and top to bottom, starting with the number 1. The central square received the number 5. If she does the same with another square board divided by 49 squares, which number will be written on the central square?

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What is the minimum number of cuts required to divide any cube into 27 smaller equal cubes?

Image Credit: Wikimedia Hexahedron.

In the single-elimination NCAA Tournament, 64 teams compete in 6 bracketed rounds. How many games are there in total?

A jigsaw puzzle contains 50 pieces. If joining any 2 pieces is considered as one move, what is the fewest number of moves required to join all fifty pieces?

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