(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