(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-4-6-
open" list. Feel free to advertise 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-4-6@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 4-6 Regular
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vertex
-> C A triangular pencil holder is marked as shown. When it is "rolled"
/ \ once to the right, A becomes the vertex and B-C the base. Use a
A - B table like the one shown, and try to discover patterns to determine
------- which letter will be the vertex after 10, 17, 23 and 30 rolls.
Table: # rolls | vertex | base (HINT: You may need to look at
-------+--------+------- a multiplication table for 3)
0 | C | A-B
1 | A | B-C
... | ... | ...
Remember to write down your steps and conclusions.
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MathMagic Cycle 25: Level 4-6 Advanced
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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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Good luck
MrH