5 digit multiplication

[MattcAnderson]

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

[blip]

Step 1: A=2

Step 2: E=8

Step 3: B=1

Step 4: D=7

Step 5: C=9

[alpertron]

Originally Posted by MattcAnderson

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].

[TheMawn]

The answer has been posted previously. I've attached a more thorough solution.

[owftheevil]

Originally Posted by MattcAnderson

There is only one set of digits that will work.

What's wrong with all zeros?

[alpertron]

Originally Posted by owftheevil

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.

[MattcAnderson]

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

[thompsonamy]

I didn't understand this puzzle, confusing. How it is zero?

[wblipp]

Originally Posted by thompsonamy

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.