Scenario: Vladimir and Alphonso are collectors of Toy Story figurines. Each has six dollar bills to spend on three figurines-Sheriff Woody, Buzz Lightyear, and Jessie-that are put up for auction where Vlad and Alph are the only bidders. They simultaneously and independently write down their bids, in whole numbers adding up to $6, for the three figurines and give them to the auctioneer. Whoever wrote the higher number for a figurine wins it. For example, if Vlad bids ($3, $1, $2), meaning $3 for Sheriff Woody, $1 for Buzz Lightyear, and $2 for Jessie, and Alph bids ($2, $3, $1), then Vlad wins Sheriff Woody and Jessie, while Alph wins Buzz Lightyear. If there is a tie, then a fair coin is flipped to determine the winner so that each bidder has 50 percent chance of winning a figurine. Vlad and Alph consider this case as "winning" a $ \frac{1}{2} $ figurine. Vlad and Alph care only about how many more, or less, figurines they win compared to the other.
-Refer to the scenario above.If Vlad bid ($2,$2,$2),then he can win at least ________,no matter what Alph does.
A) one and a half figurines
B) two figurines
C) one figurine
D) zero figurines

Question

Quizplus · Accepted Answer

With a bid of ($2, $2, $2), Vlad ensures that for each figurine, Alph cannot win more than one outright without tying on the others. If Alph bids more than $2 on any figurine, he must bid less on at least one other, leading to a tie or loss on those. Thus, Vlad wins at least one figurine outright or ties on all three, securing at least one and a half figurines overall.

Scenario: Vladimir and Alphonso Are Collectors of Toy Story Figurines 12 \frac{1}{2} 21​

Scenario: Vladimir and Alphonso Are Collectors of Toy Story Figurines $\frac{1}{2}$