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)
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MathMagic Cycle 14: Level 10-12 Regular
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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?
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MathMagic Cycle 14: Level 10-12 Advanced
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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= ...
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Good luck
MrH
PS. Soon I will need digitized pictures of each team. Please start talking
about it