How many ways are there to break up the number 64 into 10 natural summands (integers ≥ 1), whose maximum is 12? [Ways that differ only by the order of their summands do not count as different.]

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Inscribe into an acute-angled triangle ABC a triangle KLM of minimal perimeter (with its vertex K on AB, L on BC, M on CA).

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The rabbit (or Fibonacci) numbers form a sequence (a(1) = 1), 1, 2, 3, 5, 8,13,21,34,...,in which a(n)+2 =a(n+1) +a(n) for an y n=1,2,... . Find the greatest common divisor of the numbers a(100) and a(99).

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