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2008^2 hydras in the Hidro planet

Source: Cuba, Concurso Nacional 2009

February 5, 2014
combinatorics proposedcombinatorics

Problem Statement

In Hidro planet were living 200822008^2 hydras some time ago. One of them had 1 tentacle, other 2 and so on to the last with 200822008^2 tentacles. Let t(H)t(H) be the number of tentacles of hydra HH. The pairing of H1H_1 and H2H_2 (where t(H1)<t(H2)t(H_1) < t(H_2)) is a new hydra with t(H2)−t(H1)+8t(H_2)-t(H_1)+8 tentacles, in case of t(H1)=t(H2)t(H_1)=t(H_2) they die. An expedition found in Hidro the last hydra with 23 tentacles. That could be true ?
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