(01/07/97)

*************************************

MathMagic Cycle 23: Level 7-9 Regular 

*************************************
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

**************************************

MathMagic Cycle 23: Level 7-9 Advanced 

************************************** 
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.
============================
Good luck 
MrH