(10/13/97)
(Reminder to *REGISTERED* teams: You can now work with Net Team Partners
(NTPs) that are not registered, just subscribed to the "mathmagic-7-9-
open" list. Feel free to advertize your team name, location and e-mail,
along with the geographical location of the desired partner. To do so,
just send an e-mail to mathmagic-7-9@mathforum.org. PLEASE remember
this only works if you have paid and been included in one of the WELCOMES
regularly posted.)
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MathMagic Cycle 25: Level 7-9 Regular
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Ian Stewart recently wrote an article about Juniper Green (Scientific
American, March 1997) This math game uses multiplication, division (and
exponents) to encourage students to develop patterns for a winning strategy.
For our purposes, each paired team should have a 10 X 10 matrix with the
numbers 1 to 100 written on it. Decide who is going first and keep track
of the "used" numbers. The REGISTERED team can then post the exchanges
in a format similar to the examples below.
There are four rules:
1) Each team takes turns choosing one number from the matrix. Each used
number is circled and cannot be used again.
2) Apart from the opening move, each number chosen must either be an exact
divisor of the previous NTP's choice or an exact multiple.
3) The first team who is unable to choose a card looses.
4) The opening move in the challenge must be an even number - this is to
avoid the "big prime tactic" from ending the challenge too soon
As with most skill games, practice is required. There are openings and moves
that can be bad:
Move Team A Team B
1 38 : even number as required by rule # 4
2 19 : one half of move 1
3 1 : bad move!
4 97 : big prime (tactic)
5 looses : primes are only divisible by 1 (gone) and themselves
Two other examples showing some strategy:
Move Team A Team B | Team A Team B
1 22 ... | 22 ... HINT:
2 ... 11 | ... 2 Some primes and some evens
3 33 ... | 26 ... become crucial in winning -
4 ... 3 | ... 13 perhaps your team can
5 21 ... | 39 ... develop a "first-player
6 ... 7 | ... 3 strategy" to force a win...
7 35 ... | 21 ...
8 ... 5 | ... 7
9 25 ... | 35 ...
10 ... looses| ... 5
11 ... ... | 25 ...
12 ... ... | ... looses
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NOTE: This strategy game can be played by several teams simultaneously. Agree
on the order and e-mail each other each team's move. The surviving team wins.
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MathMagic Cycle 25: Level 7-9 Advanced
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Using Geoboards, rubber bands and the information given below, try to build
a formula to figure out the Area (sq. units) of any polygon using only
BOUNDARY POINTS (b) and INTERIOR POINTS (i):
+ A * B + A * * B + + + + F + + + A + +
+ * O O + * O O * + A O O O + + + O + +
+ D * * C B C O * + + B O O + F E O B C
+ + + + + + + * * + + * O O E + * O * +
+ + + + + + + + D + + C * * D + + D + +
Trapezoid ABCD Polygon ABCD Polygon ABCDEF Polygon ABCDEF
8 boundary pts. 12 boundary pts. 9 boundary pts. 8 boundary pts.
2 interior pts. 3 interior pts. 7 interior pts. 3 interior pts.
Area= 5 sq.units Area= 8 sq.units Area= 10.5 sq.u. Area= 6 sq.u.
Key: A->F: Connected boundaries; *: additional boundaries; O: interior pts;
+: grid
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Good luck
MrH