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///////////////////////////////////////////////////////////////////////////////
// Relative sizes
///////////////////////////////////////////////////////////////////////////////
// Enigma 1515 Albert Hadded, New Scientist magazine, October 11, 2008.
///////////////////////////////////////////////////////////////////////////////
// 
// In the following statements, whole numbers are expressed in words written
// in capital letters, where different letters stand for different digits, the
// same letter consistently stands for the same digit, and leading digits 
// cannot be zero.
// If the total of four BEES and a SNAIL is greater than the total of eight 
// FLEAS and an ANT; and if the total of 18 ANTS and a GNAT is greater than
// the total of 18 FLIES and a FLEA, find the value of BEETLES.
//
///////////////////////////////////////////////////////////////////////////////
//
// Solve the problem by running the query:
//
//      all Relative_sizes(beetles)
//
///////////////////////////////////////////////////////////////////////////////
//
// Results:
//
// beetles = 4335036
// ___ Solution: 1 ___ [00:00:00] __ [Backtracks: 723] ____
//
// Number of solutions: 1   Number of backtracks: 1257
// Elapsed time: 00:00:00  
//                           
///////////////////////////////////////////////////////////////////////////////

local Digit = L[0..9]

pred Relative_sizes(beetles::L) iff
    a::Digit & b::Digit & e::Digit & f::Digit & g::Digit & 
    i::Digit & l::Digit & n::Digit & s::Digit & t::Digit &

    _AllDifferent(a,b,e,f,g,i,l,n,s,t) &

    bees =          b*1000+e*100+e*10+s & b <> 0 &
    snail = s*10000+n*1000+a*100+i*10+l & s <> 0 &
    fleas = f*10000+l*1000+e*100+a*10+s & f <> 0 &
    ant =                  a*100+n*10+t & a <> 0 &
 
    4*bees + snail > 8*fleas + ant &

    ants =          a*1000+n*100+t*10+s & a <> 0 &
    gnat  =         g*1000+n*100+a*10+t & g <> 0 &
    flies = f*10000+l*1000+i*100+e*10+s & f <> 0 &
    flea =          f*1000+l*100+e*10+a & f <> 0 &
   
    18*ants + gnat > 18*flies + flea &

    beetles = b*1000000+e*100000+e*10000+t*1000+l*100+e*10+s

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