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///////////////////////////////////////////////////////////////////////////////
// Back to front
///////////////////////////////////////////////////////////////////////////////
// Enigma 1535 Bob Walker, New Scientist magazine, March 7, 2009.
///////////////////////////////////////////////////////////////////////////////
//
// Joe has found that just a few numbers have a rather unique property. 
// Reverse the order of the digits, and the new number is a multiple of the
// original. For some specified numbers of digits (four or more) there are only
// two numbers with the property.
//
// Joe gave Penny the task of finding the two 6-digit numbers.
// What is the lower 6-digit number?
//
//
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//
// Solve the problem by running the query:
//
//       all Enigma1535(y)
//
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//
// Results:
//
// y = 109989
// ___ Solution: 1 __________________________________
//
// y = 219978
// ___ Solution: 2 __________________________________
// 
// Number of solutions: 2   Number of backtracks: 809998
// Elapsed time: 00:00:00   
//
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local Di09 = I[0..9]
local Di19 = I[1..9]

pred Enigma1535(y::I) iff
    z::I & x1::Di19 & x2::Di09 & x3::Di09 & x4::Di09 & x5::Di09 & x6::Di19 &
    y = x1*100000 + x2*10000 + x3*1000 + x4*100 + x5*10 + x6 &
    z = x6*100000 + x5*10000 + x4*1000 + x3*100 + x2*10 + x1 &
    y <> z & z mod y = 0

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