Replace letters with numbers ABCD*A=EEEED

[ln]

Replace letters with numbers: ABCD*A=EEEED

[question]

I suppose that * means multiplication. Isn't it?

[Guest]

those are pretty easy actualy
it looks like 5 grade math contest the answer i believe is 3705*3=11115

[question]

The problem seems to have more than one solution.

[Guest]

it does not have more than one solution
look at it this way
Its obvious D is 0,1,5,6
Let p be a randomly selected number
A must equals 3,6,7,9 in order from A.D=pD
now if A=6 that means that D is 2,4,8 (6.2=12,6.4=24,6.8=48)
but if A=6 means that E>3 the same time it should be less than 6 becouse A=6 and it can equals 7 or more becouse 7777D:6 gives you 5 numbers
Lets say A=6 and E=4 than 4444D must be devisible by A which is 6 but D is 0,1,5,6 and 44440,44441,44445,44446 are not divisible by six ...
if A=6 and E=5 55551,55550,55555 or 55556 shoud be devisible by 5 and since it is not thats out too
so A cant be six
now if A=7 that leaves only for D to be 5 (7.5=35) but if A=7 it means 4<E<7 but E cant be 5 becouse D is 5 and thats out as well
now if A=9 means that D is 5 (9.5=45) if thats the case E should be 8 but 88885:9 does not give us an integer
So the only option that is left is A=3 if that is so
we have 3BCD.3=EEEED clearly E=1 in that case so now 1111D:3 must be an integer and an integer is devisible by 3 only when the sum of its numbers equals another integer divisible by 3 with another words 1+1+1+1+D=6 or 1+1+1+1+D=9 1+1+1+1+D=12
which leaves us D=2 , D=5 or D=8 but D can be only 0,1,5,6
so that proves that there is only one solution

[Guest]

a little mistake 11th row must be devisible by 6 becouse A=6

[Math Tutor]

It is really the most impressive proof of the problem.

[Guest]

well
probably there is a more "elegant" way to solve this but i could not come up with anything else
e mean that i found the solution really easy but when it came to proving that there is only one solution it got a lil ... long