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Old 2014-09-08, 18:35   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
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Smile 5 digit multiplication

Hi math people,

Here is another fun math puzzle.

Supply a digit for each letter sot that the equation is correct:
There is only one set of digits that will work. A given letter always represents the same digit.

A B C D E
x 4
________
E D C B A

Happy Hunting.
Regards,
Matt
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Old 2014-09-08, 19:02   #2
blip
 
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Step 1: A=2

Step 2: E=8

Step 3: B=1

Step 4: D=7

Step 5: C=9
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Old 2014-09-08, 20:35   #3
alpertron
 
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Aug 2002
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Quote:
Originally Posted by MattcAnderson View Post
Hi math people,

Here is another fun math puzzle.

Supply a digit for each letter sot that the equation is correct:
There is only one set of digits that will work. A given letter always represents the same digit.

A B C D E
x 4
________
E D C B A

Happy Hunting.
Regards,
Matt

A must be even and less than 3 (otherwise when multiplying by 4, E would be more than 9). So [B]A = 2[/B]. In the right column E = 3 or E = 8. On the left column the only correct setting is [B]E = 8[/B].

Since there is no carry to the left column, [B]B must be 1[/B] (B cannot be zero because the ending 02 is not multiple of 4). Since D8*4 = 12 we must have D=2 or D=7. On the next to the right column the only correct setting is [B]D=7[/B].

Now C*4+3 = 3C (because the carry from the second to the third column is 3), so [B]C=9[/B].

Last fiddled with by alpertron on 2014-09-08 at 20:39
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Old 2014-09-09, 01:25   #4
TheMawn
 
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The answer has been posted previously. I've attached a more thorough solution.
Attached Files
File Type: txt solution.txt (2.3 KB, 178 views)
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Old 2014-09-09, 21:47   #5
owftheevil
 
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"Carl Darby"
Oct 2012
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Quote:
Originally Posted by MattcAnderson View Post
There is only one set of digits that will work.
What's wrong with all zeros?
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Old 2014-09-09, 22:29   #6
alpertron
 
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Quote:
Originally Posted by owftheevil View Post
What's wrong with all zeros?
In this kind of puzzles any letter represent a different digit, and the leftmost digits are never zero. When using the standard rules, there is only one solution.

Last fiddled with by alpertron on 2014-09-09 at 22:30
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Old 2014-09-10, 07:12   #7
MattcAnderson
 
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"Matthew Anderson"
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Hi Math people,
There were 3 correct answers so far. Thanks for all the good work on this one. I guess the problem statement was vague when it didn't say that every letter must represent a different digit. I was just copying the problem from a book. I scanned the answer page, but it doesn't contain much more than was already stated. It is mostly a logical step by step without a lot of guessing to determine the 5 unknowns.

Keep up the good work.
Regards,
Matt
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Old 2014-12-03, 10:18   #8
thompsonamy
 
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I didn't understand this puzzle, confusing. How it is zero?
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Old 2014-12-05, 15:09   #9
wblipp
 
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May 2003
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Quote:
Originally Posted by thompsonamy View Post
I didn't understand this puzzle, confusing. How it is zero?
A=B=C=D=E=0 is mathematically true, although as noted in discussion it violates the implicit assumptions of distinct digits and no leading zeros.
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