Okay .. did you see my last answer? I think it is 5
But now I have another one and I think I know the answer but there is a trick question at the end. Maybe you can tell me if it is a trick or if it something I am missing.
A golf classic starts with 64 golfers. The golfers form pairs and each pair plays a match. The losers drop out and the winners of each pair then form new pairs and play again. Thenk those winners form pairs and play. this continues until there is one winner.
a) In how many matches must the winner play (and my answer is 5)
b)(the trick question)
How many matches are played by all the golfers to determine the winner?
Well it seems too easy to be real .. cuz I think it would be just one match since it says ALL golfers and after one match, half of them have to stop playing because they lost.
Am I right?
Thanks again.
emily
I come up with a different answer for the first question.
You start with 32 pairs. The first contest has 16 matches which yield 16 winners. The second match has 8 matches which yield 8 winners. Keep this pattern going to see if your answer is right.
You could interpret the second question in the way you did. Each golfer played at least one match. However, the question may be asking how many total matches there were before a winner was declared.
I am confused .. with 64 golfers forming pairs which equal 32, and each pair plays a match, wouldn't that be 32 matches to start with, concluding with 16 winners? ... and that set would form new partners, which would make 8 pairs ending with 4 winners, down to 2 pair with 1 winner ... what am I doing wrong? thank you for your help.
You're right, Emily. I goofed on my original figures. There were 5 matches to determine a winner.
1st match -- 32 pairs, 16 matches and 16 winners
2nd match -- 16 pairs, 8 matches and 8 winners
3rd match -- 8 pairs, 4 matches and 4 winners
4th match -- 4 pairs, 4 matches and 2 winners
5th match -- 2 pairs, 1 match and 1 winner
Thanks for catching my mistake. That's why it's always a good idea to make sure you understand an answer, no matter who tells you differently.
WoW ... You made my day! ... Thank you .. this one gets copied and printed for mom :-) .. (i keep telling her this is not 4th grade math! lol! but she likes to keep me thinking) thanks again, it is great to have people that help us! ... have a great day!
Emily
The main point, Emily, is that YOU were able to do it. Not only that, but you were confident enough to challenge my answer. And you were right! :-)
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a) To determine the number of matches the winner must play, we need to consider how many matches must be played at each stage.
In the first round, there are 64 golfers, so 32 matches must be played. In the next round, there are 32 golfers (the winners from the previous round), so 16 matches must be played. This pattern continues until there is one winner left.
Therefore, the number of matches can be calculated by summing the number of matches at each stage. In this case, it would be:
32 + 16 + 8 + 4 + 2 + 1 = 63 matches.
So, the winner must play a total of 63 matches, not 5.
b) Now let's consider the trick question. The question asks how many matches are played by all the golfers to determine the winner.
You are correct in thinking that after one match, half of the golfers will be eliminated. However, to determine the total number of matches, we need to account for all the matches played at each stage, not just the final match.
Since each pair of golfers plays a match, we can calculate the total number of matches played by summing all the matches played at each stage. In this case, it would be:
64 + 32 + 16 + 8 + 4 + 2 + 1 = 127 matches.
Therefore, all the golfers must play a total of 127 matches to determine the winner, not just one match.
So, the trick is in considering that each golfer participates in multiple matches, not just one.