 In this video we provide the solution to question number 10 for practice exam number 2 for math 1030 In which case we have six players ABCDEF who are slicing a $24 cake into six pieces using the last diminisher method with last diminisher We have to order the players and so we're just going to go in alphabetical order ABCDEF So that's the order we're going to use here. So this is the game that's been played so far We're in the middle of the game player C has already received her slice. So she's no longer in consideration For that would that happen in the first round so the first round player C got her cake now She's done now in the second round player a cut a slice of the cake because he's the one who goes first Player B then trim the cake smaller and then since there's no C in such a situation Then went to player D player D passes. So currently B is the last person to have cut the cake It's now East turn and E values the current slice of cake at five dollars and 26 cents What is E going to do now? What he does is if E values this cake at above a Fair share he's going to cut this down to a fair share Unless he's the last player to go if he's the last player to go he'll just grab what he has right there No big deal So what is a fair share right? We have six players total and there were 24 the cake is worth 24 dollars So that's the first thing to consider here If you take 24 and divided by six you end up with four dollars. So that is what a fair share is four dollars So since player E values this higher than four dollars He's not going to pass so it's not choice a he would only pass if there is If it's less than four dollars So he has to trim the cake right now if he valued it exactly at Four dollars he would trim off nothing or if he's the last player to go he would trim off nothing But player E is not the last player player F is gonna be the last player player F is still in consideration So he's not gonna trim off nothing. So how much does he trim off? Okay? So he needs to trim it down to be four dollars. So he doesn't trim off four dollars That would make that the slice only worth a dollar and twenty six cents instead. He needs to trim off a hundred and twenty six is a dollar and twenty six cents because five twenty six minus four Let's write that out there five twenty six minus four Gives a dollar and twenty six cents. That's what he cuts off so that the remaining slices worth four dollars Which is a fair share. So what what player E would do would be trim off a dollar twenty six off the cake And then depending on what F does would decide whether player E gets the cake or not But regardless what player E should do is trim off a dollar and twenty six cents