Hello Miles.

07 Sep 04 05:07, you wrote to all:

 MM> G'morning all...


 MM> Tell me,  if NINETY can be divided by nine,  TEN is one more than

 MM> a perfect square also divisible by nine - and SIX perfect squares
 MM> lie between TEN and NINETY,  how much is the ANXIETY worth ?

 MM> As usual, each capital represents a different whole digit (eg,
 MM> A=7,N...) without duplication - and the arithmetic must work...

ah the substitution game.

I'mm assuming also no leading 0s (as is usual)

for TEN-1 to be a multiple of nine, and a square it must be a (multiple of
three) squared


  X     ^2  "TEN"     NINETY

 12^2  144   145       5i541y
 15^x  225   226 bad
 18^2  324   325       5i523y
 21^2  441   442 bad
 24^2  576   577 bad
 27^2  729   730       0i037y bad
 30^2  900   901       1i109y

since NINETY is divsible by 9 that constrains I and Y so there's only
one degree freedom for each case.

  "TEN"   NINETY

   145    505413
   145    515412  bad
   145    525411  bad
   145    535410
   145    535419
   145    545418
   145    555416  bad
   145    565416  bad
   145    575415  bad
   145    585414  bad
   145    595413

   325    505233  bad
   325    515232  bad
   325    535230  bad
   325    535239  bad
   325    545238
   325    555237  bad
   325    565236  bad
   325    575235  bad
   325    585234
   325    595233  bad

   901    101097  bad
   901    111096  bad
   901    121095
   901    131094
   901    141093
   901    151092
   901    161091
   901    171090  bad
   901    171099  bad
   901    181098  bad
   901    191097  bad

so  how much is SIX  - take the bifference between the rouded-down square
roots of both

 "TEN"  NINETY  sqrt( NINETY) - sqrt(TEN)

           I        I    I=I other letters
   145    505413   698   bad
   145    535410   719   bad
   145    535419   719   bad
   145    545418   726   bad
   145    595413   759   bad
   325    545238   720   bad
   325    585234   747   bad
   901    121095   317   bad
   901    131094   332        bad
   901    141093   345        bad
   901    151092   358
   901    161091   371   bad
   TEN    NINETY   SIX
=== Cut ===

  TEN    NINETY   SIX
  901    151093   357

  0123456789
  ENYS I  XT

    ANXIETY
    ?185093

 anxiety is one of 4185093, 6185093, or 7185093.

 Unless there some other restriction you forgot to mention

Jasen

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