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Given the point

O

in the space and

1979

straight lines

l_1, l_2, ... , l_{1979}

containing it. Not a pair of lines is orthogonal. Given a point

A_1

l_1

that doesn't coincide with

O

. Prove that it is possible to choose the points

A_i

l_i

(

i = 2, 3, ... , 1979

) in so that

1979

pairs will be orthogonal:

A_1A_3

and

l_2

A_2A_4

and

l_3

...

A_{i-1}A_{i+1}

and

l_i

...

A_{1977}A_{1979}

and

l_{1978}

A_{1978}A_1

and

l_{1979}

A_{1979}A_2

and

l_1

Problem Statement