5
Part of 2001 May Olympiad
Problems(2)
1-2001 witten on board
Source: VII May Olympiad (Olimpiada de Mayo) 2001 L2 P5
9/19/2022
On the board are written the natural numbers from to inclusive. You have to delete some numbers so that among those that remain undeleted it is impossible to choose two different numbers such that the result of their multiplication is equal to one of the numbers that remain undeleted. What is the minimum number of numbers that must be deleted? For that amount, present an example showing which numbers are erased. Justify why, if fewer numbers are deleted, the desired property is not obtained.
number theorycombinatoricsgame
8 checkers' game in 1x8 board
Source: VII May Olympiad (Olimpiada de Mayo) 2001 L1 P5
9/22/2022
In an -square board -like the one in the figure- there is initially one checker in each square.
\begin{tabular}{ | l | c | c |c | c| c | c | c | r| }
\hline
& & & & & & & \\ \hline
\end{tabular}
A move consists of choosing two tokens and moving one of them one square to the right and the other one one square to the left. If after moves the checkers are distributed in only boxes, determine what those boxes can be and how many checkers are in each one.
gamecombinatoricsgame strategy