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Problems(2)
assing a number to 7 points on circle Puerto Rico OMCC TST 2018.4
Source:
9/16/2021
On a circumference of a circle, seven points are selected, at which different positive integers are assigned to each of them. Then fit simultaneously, each number is replaced by the least common multiple of the two neighboring numbers to it. If the same number is obtained in each of the seven points, determine the smallest possible value for .[hide=original wording]Sobre una circunferencia de un círculo, se seleccionan siete puntos, a los cuales se le asignan enteros positivos distintos a cada uno de ellos. Luego, en forma simultánea, cada número se reemplaza por el mínimo común múltiplo de los dos números vecinos a él. Si se obtiene el mismo número n en cada uno de los siete puntos, determine el menor valor posible para n.
combinatorics
2-player game with 4 piles of stones Puerto Rico Ibero IMO TST 2018.4
Source:
9/16/2021
There are piles of stones with the following quantities: , , and .
A legitimate move is to remove a stone from each from different piles. Two players and play in turns. begins the game . The player who, on his turn, cannot make a legitimate move, loses.
Determine which of the players has a winning strategy and give a strategy for that player.
combinatoricsgamewinning strategy