/////////////////////////////////////////////////////////////////////////////// // Dutch squares /////////////////////////////////////////////////////////////////////////////// // Enigma 1368 Richard England, New Scientist magazine, November 26, 2005. /////////////////////////////////////////////////////////////////////////////// // // Een, vier and negen are the Dutch for 1, 4 and 9; so it is appropriate that // I can make the following statement: // EEN, VIER and NEGEN are perfect squares. In this statement digits have been // consistently replaced by capital letters, different letters being used for // different digits. No number starts with a zero. // // Please send in the numerical value of the square root of (EEN x VIER x NEGEN) // /////////////////////////////////////////////////////////////////////////////// // // Solve the problem by running the query: // // all DutchSquares(x) // /////////////////////////////////////////////////////////////////////////////// // // Result: // // x = 144837 // ___ Solution: 1 ___ [00:00:00] __ [Backtracks: 483] ____ // // Number of solutions: 1 Number of backtracks: 1158 // Elapsed time: 00:00:00 // /////////////////////////////////////////////////////////////////////////////// pred DutchSquares(x:>L) iff arr::[0..]->>L[0..9] & arr = [e,n,v,i,r,g] & een = 100*e + 10*e + n & e <> 0 & vier = 1000*v + 100*i + 10*e + r & v <> 0 & negen = 10000*n + 1000*e + 100*g + 10*e + n & n <> 0 & RtlIsPowerOf2(een) & RtlIsPowerOf2(vier) & RtlIsPowerOf2(negen) & x = RtlSquareRoot(een*vier*negen)
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