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    Interesting Observation

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    • mathnerd_101M
      mathnerd_101 M0 M3
      last edited by mathnerd_101

      Did you know that any 2-digit number ending with 9 has the property: {AB}=A*B+A+B?
      For Example, 69=6x9+6+9!
      Can you prove this?

      If you see the text messages between two programmers, here are some common acronyms to know:
      imo: iteration may overload
      brb: bad recursion brb
      rofl: right-oriented frame layout

      audreyA 1 Reply Last reply Reply Quote 4
      • 西瓜西
        西瓜 M0★ M1★ M2★ M3★ M4★ M5★
        last edited by

        Proof is below:

        AB = 10A + B

        10A + B = A*B + A + B

        9A = A*B

        9 = B

        B = 9

        Hello, this is 西瓜.

        1 Reply Last reply Reply Quote 4
        • audreyA
          audrey MOD @mathnerd_101
          last edited by

          @mathnerd_101 nice question! And nice answer @西瓜 😄

          Just a tiny note: although your solution is completely correct, for more "formal" proofs you'll want to start from B = 9 and then show how you can manipulate the equation into {AB} = AB + A + B, in order to show that "any 2-digit number ending with 9 (B = 9) has the property {AB} = AB + A + B." That's just because sometimes, when you go from the property you want to prove is true, to the condition (e.g. a 2-digit number ending in 9), you might use a step that isn't reversible, like squaring both sides. (Example: squaring the "equation" 3 = -3 gives 9 = 9, which is true. But clearly, 3 =/= -3!)

          In this case, there aren't any irreversible steps - just subtracting something and dividing by something nonzero - it's just interesting to keep in mind. 🙂

          1 Reply Last reply Reply Quote 3
          • 西瓜西
            西瓜 M0★ M1★ M2★ M3★ M4★ M5★
            last edited by

            @audrey

            Thank you very much!

            Hello, this is 西瓜.

            audreyA 1 Reply Last reply Reply Quote 2
            • audreyA
              audrey MOD @西瓜
              last edited by

              @西瓜 No problem!

              1 Reply Last reply Reply Quote 2

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