Chung Kevin's favorite - (3)

Algebra Level 3

Define P ( a b c ) = a 3 + b 3 + c 3 P(\overline{abc}) = a^3+b^3+c^3 .

( P ( 352 ) = p q r P ( p q r ) = k l m P ( k l m ) = x y z \begin{array}{c}(P(352) & =& \overline{pqr} \\ P(\overline{pqr}) & = & \overline{klm} \\ P(\overline{klm}) & = & \overline{xyz} \end{array}

Input x y z \overline{xyz} .

Note: p , q , r , k , l , m , x , y , z p,q,r,k,l,m,x,y,z need not be distinct.


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The answer is 352.

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1 solution

Josh Banister
Jun 1, 2015

P(352) = 160

P(160) = 217

P(217) = 352

Isn't it astonishing? You started with 352 and ended with 352 only! Bonus for justifying this. :)

Nihar Mahajan - 6 years ago

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not clear what overline means. Should re-state problem wording.

Jose Torres Zapata - 6 years ago

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