Ahad, 27 Oktober 2013

Mathematics.. it's nothing short of magic (Part 3)


This time I won't be writing about the fact that mathematics is a wonder. Rather, why don't we (or it's you actually) try to solve a few puzzles that are directly related to mathematical reasoning. By the way, Mathematical Reasoning (Penaakulan Matematik in bahasa Melayu) is the fourth chapter in Mathematics Form 4. Try to solve the puzzles as you don't have to be a mathematician in order to find the solution. I will provide the solution to those who are willing to challenge their brains. Good Luck. By the way, maybe I should write the puzzles in bahasa Melayu..don't you think?
  1. Anda ingin mengupah seorang pekerja untuk satu bulan dengan menawarkannya upah yang berpatutan. Namun, pekerja itu mencadangkan agar dia dibayar 1 sen pada hari pertama, 2 sen pada hari kedua dan 4 sen pada hari ketiga. Upah pada  hari yang seterusnya akan menjadi dua kali ganda daripada hari sebelumnya, hinggalah tamat satu bulan. Sebagai majikan, mahukah anda menerima cadangan pekerja tersebut?

  2. Persamaan berikut nampak seperti satu bukti matematik bahawa 2 bersamaan dengan 1. Namun, ia salah sebenarnya. Kenapa?
 a = b
               aa = ab
          aa - bb = ab - bb
   (a + b)(a - b) = b(a - b)
            a + b = b
            a + a = a
               2a = a
                2 = 1