(01/07/97)
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MathMagic Cycle 23: Level 7-9 Regular
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The Old Annoying Building
A This diagram shows a very old building that has four
| |------- entrances, A,B,C and D, and four elevators, E,F,G and H.
| B The problem is that the building is so old that the
| E---F - elevators can only operate between adjacent floors. So to
| | | | go to a fifth floor (ground floor is considered first) a
| | | | patron can go A, E(1-2), F(2-3), G(3-4) and H(4-5), having
- H---G | to change elevators every floor...
D |
-------| | Under these rather annoying circumstances, please discuss
C with your NTPs the following:
a) How many ways are there to go to a second floor office?
b) How many ways into a third floor office?
c) How many ways (without repeating elevators) into a fourth floor office?
d) How does C) above change when you CAN repeat an elevator, BUT not on
consecutive floors? (say E(1-2) and E(3-4))
e) How many ways into a fifth floor office, both repeating elevators in
non-consecutive floors, and not repeating elevators at all?
f) What patterns have you and your NTPs developed? Please share with us
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MathMagic Cycle 23: Level 7-9 Advanced
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Patterns
1) Without the aid of algebra, try to find a two digit number that is
twice the sum of its digits.
2) A sequence of figures is built as follows:
x
x xxx
x xxx xxxxx etc...
Fig.1 Fig.2 Fig.3
How many "x" are there in figure 100?
3) For this pattern:
1 + 2 = 3
4 + 5 + 6 = 7 + 8
9+ 10 + 11 + 12 = 13 + 14 + 15 ...
What is the last number in the 80th row going to be?
Remember MathMagicians: share your thoughts with us.
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Good luck
MrH