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///////////////////////////////////////////////////////////////////////////////
//
// Enigma Number 1615
//
///////////////////////////////////////////////////////////////////////////////
//
// Enigma 1615, Gwyn Owen, New Scientist magazine, 29 September 2010
//
///////////////////////////////////////////////////////////////////////////////
// 
//  ENIGMA represents a six-digit number in which the digits are 
//  all different and non-zero.
//
//  When EN slides from the front to the back, the resulting six-digit 
//  number, IGMAEN, is 20 per cent larger than ENIGMA.
//
//  What is ENIGMA? 
//
///////////////////////////////////////////////////////////////////////////////
//
// Solve the problem by running the query:
//
//       all Enigma1615(enigma)
//
///////////////////////////////////////////////////////////////////////////////
//
// Results:
//
// enigma = 384615
// ___ Solution: 1 ___ [00:00:00] __ [Backtracks: 465] ____
//
// Number of solutions: 1   Number of backtracks: 495
// Elapsed time: 00:00:00 
//
///////////////////////////////////////////////////////////////////////////////

pred Enigma1615(enigma::L) iff
    letters :: [0..]->>L[1..9] & letters = [e,n,i,g,m,a] &
    enigma = e*100000 + n*10000 + i*1000 + g*100 + m*10 + a &
    igmaen = i*100000 + g*10000 + m*1000 + a*100 + e*10 + n &
    10*igmaen = 12*enigma

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