(In reply to

re(2): Disappointed! - I AM by brianjn)

I am very pleased that meanwhile I found the solution which in

my opinion provides the explanation to what has happened.

I would not call it a " slanging" match but rather presenting two

views, one based on trying to solve the problem, the other not

addressing the puzzle and referring to unrelated history and

plainly suggesting " Forget it!"

Seeing , how deeply Brian is convinced that the puzzle is impeccable, I therefore assumed that it either comes from reliable source (and perhaps something was lost or modified) or was created by brianjn, fully debugged and helas worded ambiguously (**imho**) while being absolutely **true** if interpreted as **Charlie found only after unrestricted computer search.**

I went back to my process of solution revised it and quickly found the following:

1. if we take the XandY

wording meaning" both not,but one of them yes" and the 1st statement as 1**2 ; and discount permutations there is only one set of letters to be used i.e. 023456789, = all except 1.

2. Showing that would constitute an answer.

I also found a solution, proved that 1232/2321 is the only couple eligible to represent the sums, checked the # of possible ways to permute this particular solution got 864 ways,( with AIE=(803)) and was about to post it and then saw Ch's generic solution with AIE =(704) and a quoted count 864.

- Thus my perception was that something is wrong i**n the text.**

The truth is that there are 6*6*6*2=432 permutations for each generic solution (The 1st line with 1232) and not 864 as I wrongly counted inspired by the data given and Ch's sample.

The permutation for a given AIE are:

6 for the order of the sumands

6 for the order of WTP

6 for the order of DBN

2 for the order two of the vowels(AIE) , one must be zero

432 per each generic solution , **864 in all as stated.**

I erroneously "counted twice" (added interchanging 1232 with 2321, which clearly is counted within the letter permutations)- the rest is history.

My conclusions ( I must add a disclaimer - it represents only **my** views):

1. It is a **very** nice puzzle

2. It would be much better to ask : prove that a digit 1 cannot appear in the solution set. Same goal, no ambiguity

3, "No leading zeroes". is redundant, it shows immediately

4. Same for "0-9 are available". It is a tautology.

4. The number 864, although true is optional(i.e. redundant, not needed to solve).

5. Last , but not the least : **I did nothing wrong.**

I was discouraged to present my reservations on the board, which will not preclude my further active involvement in the future.

When I quoted Seneca's "Errare humanum est" I was fully aware that it is also applicable to my humble self.

REM (2015: reread & fixed typo :Last , but not the** least** )

*Edited on ***July 18, 2015, 2:51 am**