MathDB

15

Part of 2019 India PRMO

Problems(2)

Parallel Diagonals of a 10-gon

Source:

8/11/2019
In how many ways can a pair of parallel diagonals of a regular polygon of 1010 sides be selected?
parallelpolygon
Negative Bases

Source: PRMO Leg 2 P15

8/25/2019
In base-22 notation, digits are 00 and 11 only and the places go up in powers of −2-2. For example, 1101111011 stands for (−2)4+(−2)3+(−2)1+(−2)0(-2)^4+(-2)^3+(-2)^1+(-2)^0 and equals number 77 in base 1010. If the decimal number 20192019 is expressed in base −2-2 how many non-zero digits does it contain ?
algebra