Word Arithmetic: (ENDEARED)/PATE = PATE, with remainder DCOP

[A19327]

This is a long-division problem in which letters are substituted for numbers. Solve the problem to determine the number value of each letter; and when the letters have been arranged in order from 0 to 9, they will spell out a word or words.

          PATE
     ---------
PATE )ENDEARED
      ENROI
      --------
        RPTRE
        REAEI
        ------
         DROOD
         TIANO
         -----
          DCOP

I have enclosed a drawing of the problem, and in the top right are a list of the letters used, but not in order.

 

[Steven G]

What have you tried? Where did you get stuck? You must be actively involved to receive help. Please read the posting guidelines for this forum.
Can you tell us what P*PATE equals?
How about A*PATE? (PATE)^2?
Think of PATE as 1000P + 100A +10T + E
....

 

[A19327]

What have you tried? Where did you get stuck? You must be actively involved to receive help. Please read the posting guidelines for this forum.
Can you tell us what P*PATE equals?
How about A*PATE? (PATE)^2?
Think of PATE as 1000P + 100A +10T + E
....

Ok, thanks for asking, I didnt want to put on the drawn problem or it would confuse people. This is where I am stuck. Zero HAS to be either C or N, and it makes more sense that it is N. As a result, the letter O has to be 1 and that is where I am stuck.

 

[A19327]

What have you tried? Where did you get stuck? You must be actively involved to receive help. Please read the posting guidelines for this forum.
Can you tell us what P*PATE equals?
How about A*PATE? (PATE)^2?
Think of PATE as 1000P + 100A +10T + E
....

There is something else that is getting me stuck. Given 1 should be letter O, when you look at the arithmetic at bottom where it says DROOD -TIANO. With that math, P would be one less than D right because of O being 1. If that is the case how can T be anything bc it has to be one less than D since there is no remainder does that make any sense?

 

[A19327]

What have you tried? Where did you get stuck? You must be actively involved to receive help. Please read the posting guidelines for this forum.
Can you tell us what P*PATE equals?
How about A*PATE? (PATE)^2?
Think of PATE as 1000P + 100A +10T + E
....

So, thats where I am right now. Can you help with the next ongoing steps?

 

[Steven G]

Ok, thanks for asking, I didnt want to put on the drawn problem or it would confuse people. This is where I am stuck. Zero HAS to be either C or N, and it makes more sense that it is N. As a result, the letter O has to be 1 and that is where I am stuck.

So at this point you are assuming that 0 is N. Now if in the end you get nowhere with that assumption you should then assume 0=C.
Working with 0 = N you claim that O has to be 1. Then you got stuck. So maybe you should go back to C=0.
I haven't looked at this problem yet, but will do so in about 20 minutes.
It really would help the helpers here if you do show your work so that no one has duplicate the work that you have done correctly.
We are all volunteers here and we prefer to help as many people as we can and duplicating work doesn't help. Thanks!

 

[A19327]

So at this point you are assuming that 0 is N. Now if in the end you get nowhere with that assumption you should then assume 0=C.
Working with 0 = N you claim that O has to be 1. Then you got stuck. So maybe you should go back to C=0.
I haven't looked at this problem yet, but will do so in about 20 minutes.
It really would help the helpers here if you do show your work so that no one has duplicate the work that you have done correctly.
We are all volunteers here and we prefer to help as many people as we can and duplicating work doesn't help. Thanks!

Im not sure how to go about solving this from the math part of it. In the past with these problems, I went about it from the anagram part of it, and it usually worked. This one is tough, but I dont know how to compute from the math standpoint.

 

[Steven G]

The way this forum generally works is that the poster posts their work so we can see which method they are using. Then we can point out any mistakes or give a hint on how to proceed. There are many ways to solve such problems and we just want to use your method.
I am sure that you do want help so please show us your work.

 

[A19327]

The way this forum generally works is that the poster posts their work so we can see which method they are using. Then we can point out any mistakes or give a hint on how to proceed. There are many ways to solve such problems and we just want to use your method.
I am sure that you do want help so please show us your work.

Unfortunately, I dont have any work to show. I was requesting help at least starting out. This wasnt a homework problem, this was a problem from a crossword puzzle book.

 

[stapel]

Unfortunately, I dont have any work to show. I was requesting help at least starting out. This wasnt a homework problem, this was a problem from a crossword puzzle book.

This is just a puzzler. There is no "formula" for "solving" this type of puzzler. You just have to give yourself time, and a lot of scratch paper, to try various options until you hit on one that works.

Eliz.

 

[Steven G]

Unfortunately, I dont have any work to show. I was requesting help at least starting out. This wasnt a homework problem, this was a problem from a crossword puzzle book.

You said that you concluded that some letters must be one of two letters but you have no work to show.
Personally, I am out of here.