Numerical puzzle, №4

Logic Level 3

A ‾ + B ‾ × ( C ‾ + D ‾ ) + E ‾ × ( F ‾ × ( G ‾ + H ‾ ) + I ‾ ) \overline{\textcolor{#D61F06}{A}}+\overline{\textcolor{#20A900}{B}}\times\left({\overline{\textcolor{#3D99F6}{C}}+\overline{\textcolor{#EC7300}{D}}}\right)+\overline{\textcolor{#69047E}{E}}\times\left({\overline{\textcolor{#333333}{F}}\times\left({\overline{\textcolor{grey}{G}}+\overline{\textcolor{#E81990}{H}}}\right)+\overline{\textcolor{#BA33D6}{I}}}\right) All numbers from n {n} to m {m} can be represented as sum above, where A , B , … , H , I \textcolor{#D61F06}{A},\textcolor{#20A900}{B},\dots,\textcolor{#E81990}{H},\textcolor{#BA33D6}{I} are distinct digits. What is maximal value of m − n m-n ?


The answer is 993.

Ilya Pavlyuchenko by Ilya Pavlyuchenko , 19, Russia

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1 solution

r = Union [ Table [ { a , b , c , d , e , f , g , h , i } = p ; a + b ( c + d ) + e ( f ( g + h ) + i ) , { p , Permutations [ Range [ 0 , 9 ] , { 9 } ] } ] ] ; Last [ r ] − First [ r ] ⇒ 993 r=\text{Union}[\text{Table}[\{a,b,c,d,e,f,g,h,i\}=p;a+b (c+d)+e (f (g+h)+i),\{p,\text{Permutations}[\text{Range}[0,9],\{9\}]\}]];\text{Last}[r]-\text{First}[r]\Rightarrow 993

English translation: Compute a list of all values of the expression while iterating over all permutations of integers from 0 to 9 inclusive taken 9 integer at a time, reduce the list to a sorted set of values and subtract the first value from the last value.

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