TOT 050 1983 Autumn S2 9-digits number from permutations of 1-9
Source:
August 18, 2019
9-digitnumber theorySum
Problem Statement
Consider all nine-digit numbers, consisting of non-repeating digits from to in an arbitrary order. A pair of such numbers is called “conditional” if their sum is equal to .
(a) Prove that there exist at least two conditional pairs (noting that () and () is considered to be one pair).
(b) Prove that the number of conditional pairs is odd.(G Galperin, Moscow)