MathDB

(050) 2

Part of 1983 Tournament Of Towns

Problems(1)

TOT 050 1983 Autumn S2 9-digits number from permutations of 1-9

Source:

8/18/2019
Consider all nine-digit numbers, consisting of non-repeating digits from 11 to 99 in an arbitrary order. A pair of such numbers is called “conditional” if their sum is equal to 987654321987654321. (a) Prove that there exist at least two conditional pairs (noting that (a,ba,b) and (b,ab,a) is considered to be one pair). (b) Prove that the number of conditional pairs is odd.
(G Galperin, Moscow)
9-digitnumber theorySum