Numerical puzzle, №3
Find sum of maximal and minimal value of , where are distinct digits, but .
The answer is 254.
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1 solution
Brute force using Wolfram Mathematica, but this easily could have been done in other computer languages.
Tally [ Sort [ Table [ r = p [ [ 1 ] ] + p [ [ 2 ] ] p [ [ 3 ] ] + p [ [ 4 ] ] ( p [ [ 5 ] ] + p [ [ 6 ] ] ) ; s = 1 0 0 p [ [ 7 ] ] + 1 0 p [ [ 8 ] ] + p [ [ 9 ] ] ; If [ r = s ∧ s ≥ 1 0 0 , s , Nothing ] , { p , Permutations [ Range [ 0 , 9 ] , { 9 } ] } ] ] ]
⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 1 0 2 1 0 3 1 0 4 1 0 5 1 0 6 1 0 7 1 0 8 1 0 9 1 2 0 1 2 3 1 2 4 1 2 5 1 2 6 1 2 7 1 2 8 1 3 0 1 3 2 1 3 4 1 3 5 1 3 6 1 4 0 1 4 2 1 4 3 1 4 6 1 5 0 1 5 2 5 2 9 6 8 0 7 2 8 0 8 0 4 4 4 8 5 2 4 4 4 8 4 4 2 8 1 2 8 3 6 2 4 1 6 1 2 4 4 4 1 6 1 2 4 1 6 8 ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞
Reading the Mathematica expression from left-to-right: Tally the frequencies of the sorted values of the table generated by computing the left hand side and the right hand side of the problem equation, then comparing the LHS and RHS for equality and for the RHS being greater or equal to 100, if so, then emit the RHS otherwise emit nothing by iterating over the permutations of the single digit integers taken nine digits at a time.