ThinkFun® Strategy Games Meeting
(Problem Solving)
Topic
This meeting uses two different deterministic games (games of strategy rather than chance) to demonstrate
how problem-solving skills can be put to great use in playing games.
Materials Needed
♦♦ Game boards for Swag and Hare & Hounds (One copy of each of these boards is included in the Club
in a Box Resource Kit; these boards may be photocopied for use by your students, or additional boards
may be downloaded from www.thinkfun.com/mathcounts.)
♦♦ 12 markers for each game of Swag and 4 markers for each game of Hare & Hounds (Markers can be
items such as coins, paper clips or plastic discs.)
♦♦ Copies of the Secret Strategy Sheet for each game
♦♦ Copies of the Why the Swag Strategy Works worksheet and answer key (optional)
Two Player Strategy Game
$
$
$ $
$ $
$ $
$
Place tokens on all 12 circles.
Decide who goes first.
Each turn, a player may remove as many tokens as he/she wants from one robber’s bag only.
Players take turns removing tokens. The player to remove the final token WINS!
For more information please go to: www.thinkfun.com/mathcounts
E
S
$ $
$
Your Goal: Be the player to remove the last coin (token) from the robbers’ swag bags!
To Play: 1.
2.
3.
4.
N
W
Your Goal: The Hare’s goal is to get past the Hounds. The Hounds’ goal is to trap the Hare!
To Play: 1. Decide which player will play the Hare and which player will play the 3 Hounds. Decide who moves first.
2. Place tokens (3 Hounds, 1 Hare) on the Start positions. You will need to supply your own tokens.
3. Players take turns, each time moving one token one space. Hounds may move in any direction except backward (
diagonally backward ( or ), while the Hare may move in any direction.
4. Hounds may not “stall” (move north /south ) for more than 6 moves. After 6 stalling moves, the Hare wins.
) or
For more information please go to: www.thinkfun.com/mathcounts
Meeting Plan
The following is a suggested timetable for spreading this activity over two club meetings. However,
depending on the length of your club meetings and the interest of your students, the activity certainly can
be spread across three or more meetings.
Meeting 1
1. Divide students into two teams. One team will become “Swag Experts”; the other will become “Hare &
Hounds Experts.” (Note: Swag is an easier game to master; Hare & Hounds is more complicated.)
2. To begin, teams spend a portion of the club meeting playing the game assigned to them. The Swag
Experts will all play Swag against each other in pairs; the Hare & Hounds Experts will play Hare & Hounds
against each other in pairs. (Additional game boards may be copied or downloaded from
www.thinkfun.com/mathcounts.)
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3. Once teams are familiar with their assigned game, it is
time to reveal the underlying mathematical strategy! Give the
corresponding Secret Strategy Sheet to the assigned team, and
encourage students to work together to master the strategies and
become a team of experts.
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MC05
2010–2011 MATHCOUNTS Club Resource Guide
27
Meeting 2
4. Now it’s time for your experts to face off. Organize a competition in which the two teams compete at
playing each of the two games.
a. Organize a round-robin competition pitting players from one team against players from the
other. Each pair of players plays Swag and then Hare & Hounds.
b. Each player keeps a running tally of his or her wins and losses for each head-to-head match-up.
c. After each pair is done with their head-to-head match-up, have students rotate so that each
Swag Expert is paired with a Hare & Hounds Expert he or she has not yet played.
d. Continue the competition as time permits or until each Swag Expert has been paired against
each Hare & Hounds Expert for a head-to-head match-up.
5. At the end of the competition, compile team results by using a chart like that shown below. Invite
students to evaluate and discuss whether “expert” players who studied the mathematical patterns fared
better at their assigned game.
Game
Swag
Hare & Hounds
Team: Hare & Hounds Experts
Wins
Losses
I
IIII IIII II
IIII IIII IIII II
II
Team: Swag Experts
Wins
Losses
IIII IIII II
I
II
IIII IIII IIII II
Optional Extensions
1. Switch roles.
a. Have teams switch Secret Strategy Sheets and study the other game, or have students form
pairs so that each pair has an “Expert” at each game. Allow time for each student to teach the
strategy to his or her partner.
b. Hold a second competition using the same round-robin and tracking system.
c. Compile and evaluate results at the end of this competition. Are the two teams more evenly
matched now that each has studied both game strategies?
2. Examine the reasoning behind the Swag strategy.
After becoming familiar with the strategies from the Swag Secret Strategy Sheet, students should
develop a chart that shows how the 5-4-1 pattern always leads to one of the other five winning
patterns. A worksheet for students is shown on the next page. The worksheet and its answer key
are available at www.thinkfun.com/mathcounts.
Possible discussion questions for this extension:
a. How many distinct moves are possible for your opponent when faced with the 5-4-1 pattern? b. If your opponent takes two coins from the first bag, does it matter which two?
c. Can a similar chart be done for each of the other five winning patterns?
d. Once you create the 5-4-1 pattern, in how many distinct ways can the remainder of the game play out?
To further explore the principles underlying these games and help
students have fun with other mathematical strategy games,
visit www.thinkfun.com/mathcounts.
28 2010–2011 MATHCOUNTS Club Resource Guide
Swag Worksheet
Why the Swag Strategy Works
Name ______________________________
You have just completed your turn, and it is now your opponent’s turn. He
or she is faced with 5 coins, 1 coin and 4 coins. Let’s see why you are now
guaranteed of being able to create another winning pattern on your next turn.
What are your opponent’s options when faced with the 5-4-1 pattern? Then what should your next
move be? And finally, what is the resulting pattern?
Row 1 shows that your opponent could take 1 coin from the first bag (the coin with the white X). Then your correct move is to
take 1 coin from the second bag (shown as the coin with the two white slashes), which results in the winning pattern 4-4.
Row 2 shows that your opponent could take 2 coins from the first bag. Then your correct move is to take 2 coins from the third
bag, which results in the winning pattern 3-2-1.
The rest of the rows need to be filled in to show the rest of your opponent’s possible moves when faced with the 5-4-1 pattern,
what your move should then be and what the final result would be. You can use a marker or highlighter to identify the coins
that are being removed and then color in the remaining coins in the last column.
Swag Worksheet
Why the Swag Strategy Works
Answer Key
Name ______________________________
You have just completed your turn, and it is now your opponent’s turn. He
or she is faced with 5 coins, 1 coin and 4 coins. Let’s see why you are now
guaranteed of being able to create another winning pattern on your next turn.
What are your opponent’s options when faced with the 5-4-1 pattern? Then what should your next
move be? And finally, what is the resulting pattern?
Row 1 shows that your opponent could take 1 coin from the first bag (the coin with the white X). Then your correct move is to
take 1 coin from the second bag (shown as the coin with the two white slashes), which results in the winning pattern 4-4.
Row 2 shows that your opponent could take 2 coins from the first bag. Then your correct move is to take 2 coins from the third
bag, which results in the winning pattern 3-2-1.
The rest of the rows need to be filled in to show the rest of your opponent’s possible moves when faced with the 5-4-1 pattern,
what your move should then be and what the final result would be. You can use a marker or highlighter to identify the coins
that are being removed and then color in the remaining coins in the last column.
Opponent’s Move
My Move
Result
1.
4-4
2.
3-2-1
3.
3-2-1
4.
1-1
5.
1-1
6.
4-4
7.
3-2-1
8.
3-2-1
9.
1-1
10.
1-1