5
Part of 2009 May Olympiad
Problems(2)
Any ideas???
Source: May Olympiad(Olimpiada de Mayo) 2009
5/10/2018
A game of solitaire strats of with cards. Some are facing up and sum are facing down.
In each move a card that's facing up should me choosen, taken away, and turning over the cards next to it (if there are cards next to it). The game is won when you have accomplished to take all the cards from the table.
If you initially start with cards facing up, find all the values of such that the game can be won. Explain how to win the game, independently from the initial placement of the cards facing up, justify your answer for why it is impossible to win with other values of .
Two cards are neighboring when one is immediately next to the other, to the left or right.Example: The card marked has two neighboring cards and the one marked with only a has only one neighboring card. After taking a card there is a hole left, such that the card marked has only one neighboring card, and the one marked does'nt have any.
combinatorics
add walks on grid 55 lines x 45 lines
Source: XV May Olympiad (Olimpiada de Mayo) 2009 L1 P5
9/22/2022
An ant walks along the lines of a grid made up of horizontal lines and vertical lines. You want to paint some sections of lines so that the ant can go from any intersection to any other intersection, walking exclusively along painted sections. If the distance between consecutive lines is cm, what is the least possible number of centimeters that should be painted? What is the higher value?
combinatorics