MOON + SOON + NOON = JUNE: Find letter values

[defeated_soldier]

  M O O N
+ S O O N
+ N O O N
  -------
  J U N E

What is the value of U + N + E, if each letter represents a distinct digit from 1 to 9?

(a) 11
(b) 13
(c) 14
(d) No unique value exists.

My book has given a very big solution to get the answer. However, can I use some smarter technique to eliminate and find out the correct choice out of these given options? Any tricks or hints would be appreciated!

 

[Denis]

Those are "puzzles" known as alphametics; google search "alphametics".

M O O N
S O O N
N O O N
----------
J U N E

Solving involves lots of logic, like:
N <> 0 or 5
if N<4 then 3N=E
if N=4 or 6 then 3N=10+E
if N>6 theb 3N=20+E

 

[stapel]

Since there is no nice neat formula for this sort of exercise, a "big long solution" is pretty much all there is, being the explanation of the "intelligent guess-n-check" required for solving this.

For instance, you see that you are adding three four-digit numbers and getting a four-digit number. This tells you that M + S + N (plus whatever "carry" there might be from the tens' to the hundreds' place) must be 9 or less. So this puts a cap on that sum.

You know that, whatever E is, it is the ones' digit of 3N. So look at the options for 3N:

. . . . .3, 6, 9, 12, 15, 18, 21, 24, 27

Then work through the options, working with 3N, E, and 3O. And so forth.

Yes, it's long and involved. The point (I think) is that you learn to work logically, so that you can find a solution with a minimal amount of effort.

Eliz.

 

[defeated_soldier]

this seems very difficult problem to solve.

however, from your comments i can deduce that U,N,E might be multiple of 3
but that does not gives me the sum of J , U,N,E .

Thanks for the information . i can i have no shortcuts to choose the answer but to adapt the book's lengthy solution