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BALTIC-WAY 2001 Problem 20

  • Answer

From a sequence of integers (a,b,c,d)(a, b, c, d) each of the sequences

(c,d,a,b),(b,a,d,c),(a+nc,b+nd,c,d),(a+nb,b,c+nd,d),(c, d, a, b),(b, a, d, c),(a+n c, b+n d, c, d),(a+n b, b, c+n d, d),

for arbitrary integer nn can be obtained by one step. Is it possible to obtain (3,4,5,7)(3,4,5,7) from (1,2,3,4)(1,2,3,4) through a sequence of such steps?

Dataset text NuminaMath olympiads. Quoted with source.

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no

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