Substitute each of the capital letters in bold by a different base ten digit from 0 to 9 to satisfy this alphametic equation. Neither P nor O can be zero.

PANE = [OUTSHOUT/ PIANO], where the remainder obtained upon dividing OUTSHOUT by PIANO is less than 500.

Note: [x] denotes the greatest integer ≤ x.

I set up a spreadsheet *:

A E H I N O P S T U
7 5 2 8 6 9 1  3 0 4
6 0 4 9 7 3 1  5 8 2

and mirrored values assigning them to:
P A N E
1 7 6 5
1 6 7 0

O U T S H O U T
9  4 0 3 2 9  4 0
3  2 8 5 4 3  2 8
and
P I A N O
1 8 7 6 9
1 9 6 7 3

Dividing OUTSHOUT by PIANO produced a compound number.  I multiplied the decimal part by PIANO to get the remainder.

Playing with this arrangement I found:
         PANE            1765
OUTSHOUT     94032940
       PIANO          18769  with a remainder of 250.

That said I put Daniel's values through my spreadsheet which by confirming his result also confirmed that I had no error in my spreadsheet construction.

I have copied his program listing directly into QuickBasic and it yielded just his result.  Reviewing that listing I cannot see why that was missed.  (see below)

* In the top half of this comment I have recorded my values as being underlined and the values Daniel derived are below them.

Charlie, in the comment which follows pointed out my oversight, I've addressed that in the comment following his.

Edited on August 13, 2009, 2:47 am

Posted by brianjn on 2009-08-13 01:50:36