MathDB

The fields of the

8\times 8

chessboard are numbered from

1

64

in the following manner: For

i=1,2,\cdots,63

the field numbered by

i+1

can be reached from the field numbered by

i

by one move of the knight. Let us choose positive real numbers

x_{1},x_{2},\cdots,x_{64}

. For each white field numbered by

i

define the number

y_{i}=1+x_{i}^{2}-\sqrt[3]{x_{i-1}^{2}x_{i+1}}

and for each black field numbered by

j

define the number

y_{j}=1+x_{j}^{2}-\sqrt[3]{x_{j-1}x_{j+1}^{2}}

where

x_{0}=x_{64}

and

x_{1}=x_{65}

. Prove that

\sum_{i=1}^{64}y_{i}\geq 48

5