Power Tower Luck

Algebra Level 4

Tommy incorrectly thinks that abc=(ab)c,\Large \color{#3D99F6}{a}^{\color{#20A900}{b}^{\color{#D61F06}{c}}}= \left(\color{#3D99F6}{a}^{\color{#20A900}{b}}\right)^{\color{#D61F06}{c}}, while Jenny correctly knows that abc=a(bc).\Large \color{#3D99F6}{a}^{\color{#20A900}{b}^{\color{#D61F06}{c}}}= \color{#3D99F6}{a}^{\left(\color{#20A900}{b}^{\color{#D61F06}{c}}\right)}.

For how many of the 64 ordered triples of positive integers less than or equal to 4, (a,b,c){1,2,3,4}3,(\color{#3D99F6}{a},\color{#20A900}{b},\color{#D61F06}{c}) \in \{1,2,3,4\}^3, will Tommy's incorrect method get the correct answer?

×

Problem Loading...

Note Loading...

Set Loading...