MathDB

1

Part of 2021 Bolivian Cono Sur TST

Problems(3)

True coin, there is 1 fake coin AMONG US. Can u find the SUSSY impostor?

Source: Bolivian Cono Sur TST 2021 Day 1 P1

11/17/2021
a) Among 99 apparently identical coins, one is false and lighter than the others. How can you discover the fake coin by making 22 weighing in a two-course balance? b) Find the least necessary number of weighing that must be done to cover a false currency between 2727 coins if all the others are true.
combinatoricscoinsBoliviaCono Sur TSTTST
Finding all possible $n$ on a strange division condition!!

Source: Bolivian Cono Sur Pre-TST 2021 P1

11/12/2021
Find the sum of all positive integers nn such that n+11n−1\frac{n+11}{\sqrt{n-1}} is an integer.
Pre TSTTSTBoliviaCono Sur TSTnumber theoryDivisibility
When a congruence plays Hide N Seek on a rhombus. Can u find it :D?

Source: Bolivian Cono Sur TST 2021 Day 2 P1

11/17/2021
Inside a rhombus ABCDABCD with ∠BAD=60\angle BAD=60, points F,H,GF,H,G are choosen on lines AD,DC,ACAD,DC,AC respectivily such that DFGHDFGH is a paralelogram. Show that BFHBFH is a equilateral triangle.
geometryrhombusparallelogramEquilateral TriangleBoliviaCono Sur TSTTST