This document discusses logical reasoning and provides 3 examples of problems solved through logical reasoning. Logical reasoning involves breaking down problems into logical steps and using techniques like deduction and contradiction to arrive at solutions. The first example asks if 44 silver dollars can be distributed into 10 pockets with each pocket containing a different number of dollars. The second example asks if a notched checkerboard with squares removed can still be covered with the remaining dominoes. The third example asks if the equation x2 + y2 = 3(u2 + v2) has any integral solutions other than (0, 0, 0, 0). The document concludes by listing references on problem solving strategies and mathematical methods.

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.
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3. Logical Reasoning
Proving by deduction
Proving by contradiction
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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?
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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?
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6. Logical Reasoning -
Example 2
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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 ).
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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.