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Old 02-23-2003, 04:53 PM   #1 (permalink)
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Default It's amazing!!!

Can you determine how this works??? Betcha can't...
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Old 02-23-2003, 06:40 PM   #2 (permalink)
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Default Pretty Cool

Yes and No, Actually, my sixteen year old math whiz figured it out in one try. As soon as he showed it to me, it was "Duhhhhhhhhhh!" Still pretty cool, nonetheless.
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Old 02-23-2003, 06:40 PM   #3 (permalink)
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Every possible value that you could reach has the same symbol each time. It is a bit confusing becasue the "chosen" symbol is generated randomly.
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Old 02-23-2003, 06:45 PM   #4 (permalink)
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Every 9th digit has the same value (0,9,18,27,36, etc.). These are the only possible numbers that you can reach using the formula provided.
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Old 02-23-2003, 08:12 PM   #5 (permalink)
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An old parlor trick called "casting out nines" where all the symbols shown for any two digits adding to nine have the same symbol - cleverly, the symbol changes every time so it's harder to track. Note that all the symbols where the digits sum to 9 are identical before you click on the crystal ball.

Subtracting the sum of (a+b) from a number ab gives you two digits that add to nine since:

ab - (a+b)) = 10a + b - (a+b) = 10a - a + b - b = 9a

since a can only be an integer in the decimal system , the answer 9a is always a multiple of the integer 9

since the original number has two digits, a>0

the only possible sets of numbers that can meet this criteria are

1 X 9 = 09
2 X 9 = 18
3 X 9 = 27
4 X 9 = 36
5 X 9 =45
6 X 9 = 54
7 X 0 = 63
8 X 9 = 72
9 X 9 =81

Probably more than you ever wanted to know...
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Old 03-21-2003, 05:57 PM   #6 (permalink)
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1. Focus on the dot in the center.
2. Then move your head forward and backwards to/from the monitor screen.
3. Weird, huh???
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Old 03-21-2003, 06:07 PM   #7 (permalink)
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Default Eye Examination Chart

Increase your distance from the chart until it is readable.....
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