Grades 5-6 Video Solutions 2021-video 2021 5-6/17

Video Transcription

17. Ranya had 4 white tokens and Wanya had 4 grey tokens. They played a game in which they took turns to place one of their tokens to create 2 piles. Ranya placed her first  token first. Which pair of piles could they NOT create? Since Ranya placed her token white first, Wanya must have placed hers, grey, last.  So what does that mean? That means that the last token placed has to be somewhere on the top. And at least one of the topmost tokens must be grey. This is the case in every single  answer except for E. So in A we can say ok the last token that was placed down must be this one here, this top grey. In B the last one placed is this one. C the last one placed  this one. D here. But in E the last one placed can't be on this third row because something must clearly be placed after it. The answer is therefore E.

Video Summary

In a game where Ranya and Wanya alternately placed tokens to create two piles, the goal was to determine which configuration was impossible. Ranya, with white tokens, started, and Wanya, with grey tokens, placed the last token. For every possible configuration, the topmost token must be grey, indicating Wanya's last move. However, in configuration E, the top token isn't grey, making it impossible according to the game's rules. Therefore, the configuration they could not create is E.

Keywords

game rules

token placement

Ranya and Wanya

impossible configuration

configuration E