MathDB

4

Part of 2015 India Regional MathematicaI Olympiad

Problems(5)

RMO Delhi Q.4

Source:

12/20/2015
4. Suppose 36 objects are placed along a circle at equal distances. In how many ways can 3 objects be chosen from among them so that no two of the three chosen objects are adjacent nor diametrically opposite.
combinatorics
28 objects are placed along a circle at equal distances, choose 3

Source: CRMO 2015 region 1 p4

9/30/2018
Suppose 2828 objects are placed along a circle at equal distances. In how many ways can 33 objects be chosen from among them so that no two of the three chosen objects are adjacent nor diametrically opposite?
combinatoricscombinatorial geometrycircle
Question 4

Source:

12/6/2015
Suppose 32 objects are placed along a circle at equal distances. In how many ways can 3 objects be chosen from among them so that no two of the three chosen objects are adjacent nor diametrically opposite?
RMO 2015
40 objects are placed along a circle at equal distances, choose 3

Source: CRMO 2015 region 4 (Karnataka) p4

9/30/2018
Suppose 4040 objects are placed along a circle at equal distances. In how many ways can 33 objects be chosen from among them so that no two of the three chosen objects are adjacent nor diametrically opposite?
combinatoricscombinatorial geometrycircle
3 three digit numbers (cyclic digits arrangement) in GP

Source: RMO (Mumbai Region) 2015 P4

12/6/2015
Find all three digit natural numbers of the form (abc)10(abc)_{10} such that (abc)10(abc)_{10}, (bca)10(bca)_{10} and (cab)10(cab)_{10} are in geometric progression. (Here (abc)10(abc)_{10} is representation in base 1010.)
geometric sequencenumber theoryalgebranumber theory proposed