Problems and Problem Solving - Ministry of Education

Three cups of different colours (red, blue and green) are on a table; each cup
has an object in it – either a coin, a bean or a shell. You are told the following:
To the left of the red cup is the green cup.
To the left of the bean is the coin
To the right of the shell is the blue cup
To the right of the blue cup is the bean
Identify which object is in each cup.
Games
Many problems are derived from game situations. Games that create problems are those in which
a winning strategy is to be established by the players so that, regardless of what an opponent
does, a particular series of plays will ensure that one person will always win. A winning strategy
usually consists of:
a)
b)
a rule as to who plays first; and
a sequence of moves that guarantees a victory for one player.
The derivation of the winning strategy, however, is the search for a solution and will require the
players to employ many problem-solving heuristics. The Spiral Game, on the following page, is an
example of a mathematics game that is problematic.
Instructions:
a. This is a game for two players. Each player will take turns in moving a counter
around the board from start to end.
b. A counter is placed on number 1 – only one counter is to be used (do not use
one counter for each player). Each player will take turns moving the same
counter around the board.
c. The player who chooses to go first will move the counter between 1 and 6 dots
d. Player 2 now moves the counter from where player 1 leaves it; he also has to
move it between 1 and 6 dots.
e. Each player will continue taking turns moving the counter between 1 and 6
dots along the spiral; turning back is not allowed.
f. The winner is the player who moves the counter on dot number 25. Try to find
a winning strategy.
18 PROBLEMS AND PROBLEM SOLVING
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