Grades 5-6 Video Solutions 2023-2023_1-2

Video Transcription

Question 28. Sonja and Robert are playing a game. They can alternately take 1, 2, 3, 4, or 5 tiles from a pile of tiles.  Whoever takes the last tile or tiles loses. At one point of the game, there are 10 tiles left in the pile, and it is Sonja's turn to take some tiles.  How many tiles should Sonja leave for Robert to be sure that she will win? It is important to note that you can only take 1, 2, 3, 4, or 5 tiles. You cannot take 0.  So if you leave your opponent with 1 tile left, they will have to take it and lose. So if you end up with 1 tile, that will be a losing tile.  If you are left with 2 tiles, you could take 1 tile and leave your opponent with the other tile. If you are left with 3 tiles, you could take 2 and leave them with the 1.  This is true all the way up to the point that if you had 6 tiles, you could take 5 and leave your opponent with the 1.  So we know for sure that the answers can't be E or D, since if they were left with 5 or 6 tiles, they would make Sonja lose.  However, if there was 1 more tile, 7 tiles, at most, Robert would be able to take 5, leaving Sonja 2 tiles. She could then take 1 and force him to take the last one.  If Robert took 1 tile, it would leave Sonja with 6 tiles, and she could leave him with 1 tile by taking 5. So, to make sure that Robert loses, Sonja has to leave him with 7 tiles.  So our answer will be C.

Video Summary

In the game between Sonja and Robert, they can take 1 to 5 tiles on their turn, and the player forced to take the last tile loses. With 10 tiles remaining, it’s Sonja’s turn. To ensure her victory, Sonja should leave Robert with 7 tiles. This is because, with 7 tiles, Robert will eventually be forced into losing positions where Sonja can ensure he ends up taking the last tile. Hence, by leaving him with 7 tiles, Sonja can secure a guaranteed win.

Keywords

game strategy

Sonja vs Robert

tile game

winning tactics

forced loss