Maximize the Product

Algebra Level 3

If each variable represents a distinct digit, what is the maximum value for the cryptogram product:

A B × C D \begin{array} { l l l } & A & B \\ \times & C & D \\ \hline \\ \end{array}

97 × 86 97 \times 86 96 × 87 96 \times 87 98 × 76 98 \times 76

Chung Kevin by Chung Kevin , 45, Australia

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1 solution

Anirudh Sreekumar
Mar 22, 2017

98 × 86 − 86 > 98 × 86 − 980 98\times86-86>98\times86-980

⟹ 97 × 86 > 98 × 76 \implies 97\times86>98\times76

Also,

97 × 87 − 87 > 97 × 87 − 97 97\times87-87>97\times87-97

⟹ 96 × 87 > 97 × 86 \implies 96\times87>97\times86

Thus, 96 × 87 > 97 × 86 > 98 × 76 96\times87>97\times86>98\times76

0 Helpful 0 Interesting 0 Brilliant 0 Confused

That's a nice way to compare them without having to multiply out all of the values :)

Chung Kevin - 4 years, 2 months ago

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