Date: Mon, 30 Jan 1995 23:47:16 -0600 (MDT) From: "Alan A. Hodson" Subject: [MM-102] Challenge # 14 To: mathmagic-10-12@mathforum.org (1/30/95) *************************************** MathMagic Cycle 14: Level 10-12 Regular *************************************** Correcting the "spelling" of an equation Almost any 5th grader should be able to show that the following equation is not true: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 100 Using only + and - signs, change the spacing between the numbers on the left side to allow for bigger numbers, without changing the order of the digits or the result: 123 + 45 - 67 + 89 = 100 Between your team and your NTPs you should be able to create at least six more equations. Can you do the same for the reverse ordered digits? 98 + 76 ... = 100? If each possibility is one point, what was your score? **************************************** MathMagic Cycle 14: Level 10-12 Advanced **************************************** Xmas Tree Table Last Xmas when I was placing a small round table in the corner where the tree seems to look its best I noticed a dent on the side of the table. As I turned the table (it touches both walls) I began wondering if I could tell the radius of the table by the position of the dent. The dent was first 80 cm from one wall and 90 from the other, but I moved it so that the dent didn't show as much. It ended at 20 cm and 90 cm from each wall. After some work I figured the table radius could be 50 cm, and when I actually measured it, the diameter was indeed one meter. What kind of calculations did I do? 10 A= SQR(2*(... Hints: Try a scale drawing first. The pieces of the 20 B= X1 + X2 BASIC program I wrote for it are also a good 30 R1= ... lead 40 R2= ... ================== Good luck MrH PS. Soon I will need digitized pictures of each team. Please start talking about it