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Re: Base function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88180] Re: Base function
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sun, 27 Apr 2008 04:59:35 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fuumbc$88b$1@smc.vnet.net>

haitomi wrote:

> ((1*12 + 4)*11 + 4)*10 + 4
> 
> 1804
> 
> I need help with a function find the Calander "base"
> 
> Cbase[1804,{12,11,10}]
> 
> out put will be
> {1,4,4,4}

Since the above (incomplete) assignment sounds like homework, I shall 
suggest, without further explanation, one possible coding for such a 
function.

cBase[d_Integer?NonNegative,
   l : {a_, b_, c_} /; VectorQ[l, IntegerQ@# && Positive@# &]] :=
  Module[{v = {e, f, g, h}},
   v /. ToRules@
     Reduce[c (a b e + b f + g) + h == d && And @@ Thread[0 <= v <= 9],
       Integers]]

cBase[1804, {12, 11, 10}]

{1, 4, 4, 4}

Note that the code above does not attempt to handle in any specific way 
cases where no solution or multiple solutions may arise.

Regards,
-- Jean-Marc


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