MathDB

1

Part of 2012 Bundeswettbewerb Mathematik

Problems(2)

16 digits in a row, add a colon for a division, can result be 2?

Source: Germany Federal - Bundeswettbewerb Mathematik 2012, round 1, p1

4/11/2020
Alex writes the sixteen digits 2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,92, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9 side by side in any order and then places a colon somewhere between two digits, so that a division task arises. Can the result of this calculation be 22?
number theoryDigitsDivision
subdivision of {1,2,..,2n}

Source:

8/19/2015
given a positive integer nn. the set {1,2,..,2n}\{ 1,2,..,2n \} is partitioned into a1<a2<...<ana_1<a_2<...<a_n and b1>b2>...>bnb_1>b_2>...>b_n. find the value of : ∑i=1n∣ai−bi∣ \sum_{i=1}^{n}|a_i - b_i|
number theoryalgebra