Latest Maths Olympiad Aptitude Question SOLUTION: Suppose the integers 1, 2, 3, . . . , 10 are split into two disjoint collections a1, a2, a3, a4, a5 and b1, b2, b3, b4, b5 such that a1 < a2 < a3 < a4 < a5, b1 > b2 > b3 > b4 > b5.

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(#M40021961) MATHS OLYMPIAD question ALGEBRA Keep an EYE

Suppose the integers 1, 2, 3, . . . , 10 are split into two disjoint collections a1, a2, a3, a4, a5 and
b1, b2, b3, b4, b5 such that
a1 < a2 < a3 < a4 < a5,
b1 > b2 > b3 > b4 > b5.
(i) Show that the larger number in any pair {aj , bj}, 1  j  5, is at least 6.
(ii) Show that |a1-b1|+|a2-b2|+|a3-b3|+|a4-b4|+|a5-b5| = 25 for every such partition.

Asked In Maths Olympiad MAN (11 years ago)

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