1. Logical Reasoning
Tsang Yiu Ping (09451745)
Wong Hang Chi (09451331)
Logical Reasoning – p.

2. Problem-solving by
Logical Reasoning
Discussion with friends/plan a strategy for a
work plan → Predict a conversation or a
potential discussion/argument.
A −→ B −→ C −→ D.
Strength of an argument depends on the
validity of the logical reasoning used.
Logical Reasoning – p.

3. Logical Reasoning
Proving by deduction
Proving by contradiction
Logical Reasoning – p.

4. Logical Reasoning -
Example 1
Bob has 10 pockets and 44 silver dollars. He
wants to put his dollars into his pockets so
distributed that each pocket contains a different
number of dollars. Can he do so?
Logical Reasoning – p.

5. Logical Reasoning -
Example 2
A domino can cover exactly 2 adjacent squares
on a standard checkerboard. Thus, 32 dominoes
will exactly cover the 64 squares on the
checkerboard. Suppose we now remove one
square from each of the two diagonally opposite
corners of the checkerboard and remove one
domino as well. Can you now cover this
“notched” checkerboard with the 31 remaining
dominoes? Why or why not?
Logical Reasoning – p.

6. Logical Reasoning -
Example 2
Logical Reasoning – p.

7. Logical Reasoning -
Example 3
Show that the following equation has no integral
solution except (x, y, u, v) = (0, 0, 0, 0).
2 2 2 2
x + y = 3(u + v ).
Logical Reasoning – p.

8. References
Posamentier, A. S. & S. Krulik. (1998).
Problem solving strategies for efficient and
elegant solutions : a resource for the
mathematics teacher. Thousand Oaks, CA :
Corwin Press.
Pólya, George. (1990). How to solve it : a
new aspect of mathematical method (2nd
ed.). London : Penguin Books.
恩格爾著，舒五昌、馮志剛譯(2004)。《解決
問題的策略》上海，上海教育出版社。
Logical Reasoning – p.