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12-11-2004 02:28 PM  13 years agoPost 1
rchelipilot121

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In the multiplication shown below, the digits have been replaced by letters: different letters represent different digits. The same letters represent the same digits.

ABCDE
x..........4
EDCBA


What was the original multiplication?

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12-12-2004 09:57 AM  13 years agoPost 2
Colibri

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The Netherlands

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The answer is:

21978
x.......4
87912

This actually works for:
21n78
x.......4
87n12

where n can be any number of 9's so it works for

2178, 21978, 219978, 2199978 etc.

If you do the multiplication manually on paper you will see why this is the case.

One other thing to notice is that 21 + 78 is 99 and 87 + 12 is 99 too. So this must be some kind of magic number.

Tim

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12-12-2004 10:51 AM  13 years agoPost 3
noname

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Woodinville, WA

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EDCBA = 87912

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12-13-2004 11:53 PM  13 years agoPost 4
Hawk4flyer

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Deland,Florida

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Its the magic of digital primes.....


cool party trick....

ask someone to think of a number, any number...

ask the to multiply that number by ( arbitrary ) 117 or 108 or 126...

or any multiple of 9....

tell them to write the number down. Then remove one digit thats NOT a zero or a nine.

ask them to tell you the remaining digits. ( they don't have to be in order either.)

add those remaining digits together until you reach a single digit.

for example....

12345 * 108 = 1333260
1333260 remove the 6 and you have 133320

1+3+3+3+2+0 = 12 .... 1+2 = 3

3 is the sigular digit.

Now subtract 3 from 9 and you have the missing digit.

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12-14-2004 07:03 AM  13 years agoPost 5
Colibri

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The Netherlands

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Interesting. So if you multiply any number by 9^n where n>0 the sum of the digits is always 9.

Tim

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