Stuart's Spectacular Students

This is dedicated to my amazing students. The goal is for each and every one of them to feel unstoppable by the time they walk out of the classroom door for the final time in May. This chronicles their journey; their own Chronicles of Self-Actualization.

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Wednesday, May 09, 2007

Holy Cow! A Brand New Feature

We just keep getting more and more fortunate. Mr. Haney, the Director of Operations Engineering for Lockheed Martin, has sent in some wonderful math problems for you to solve. Let's see who can come up with an answer first! Remember to explain how you arrived at your answer.


A farmer brings his cows to market for sale.
The 1st buyer buys half of the farmers cows, plus 1/2 a cow.
A 2nd buyer buys half of the remaining (after the 1st buyer) cows, plus 1/2 a cow.
The 3rd and final buyer buys half of the remaining (after the 1st and 2nd buyers) cows, plus 1/2 a cow.
All three buyers bought whole cows.
The farmer sold all of his cows he brought to market.

How many cows did the farmer bring to market?

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35 Comments:

  • At 2:44 PM , Anonymous ryan said...

    That is a very hard question, but my father and I figured you need an odd number and when you get half of that number they buy 1/2 cow that makes a whole number, but that whole number must be another odd and that needs to happen for four farmers.

     
  • At 7:56 PM , Anonymous Mahrukh said...

    This is a tough one, but alot similar to monkey coconut one. Intresting, I wll try figuring this out, but later.

     
  • At 11:28 AM , Anonymous Bridget And You better read this! said...

    Serena is letting the boy's use our puter, and they are only gonna play games, and we need to work on educational stuff! We need to get this project done by the end of the year!

     
  • At 11:31 AM , Anonymous Jess said...

    The only way that someone could have bought half a cow ,and still have it in one piece, then that person would have needed to split the payment with someone else. Curious.

     
  • At 11:33 AM , Anonymous dallas said...

    I think he sold 3 and a 1/2 cows at the market

     
  • At 11:33 AM , Anonymous ZAK said...

    I think the answer is 12 and a 1/2 cows that the farner brought to the market!

     
  • At 11:37 AM , Anonymous Bridget And Jess said...

    Well, if the farmer got one half of a cow, he'd have to split it with another farmer. The lucky farmer would get the head.

     
  • At 11:39 AM , Anonymous Anonymous said...

    we no la answer is 5 because it is

     
  • At 11:41 AM , Anonymous mark said...

    i think it is 10 and a half.

     
  • At 11:45 AM , Anonymous Anonymous said...

    from: wintwin & Ryan
    The answer is the amount of cows the farmer brought to the market is all of the cows that he sold.

     
  • At 11:49 AM , Anonymous Jess said...

    9, because half of 9 is 41/2,which is what the first farmer bought. The farmer bought half because he had shared the price,or he got a deal. The next farmer comes and buys the next half, or 21/2, getting the same deal, buying the half that the last farmer didn't. The last comes and does the same thing, buying 11/2.

     
  • At 12:05 PM , Anonymous dallas helped by jessica said...

    I think its 9 because the first guy bought hafe of the cows.The second guy bought hafe of the remaining cows.The third guy bought hafe of the remainging cows.So 9/2 is 4 1/2,so 4 1/2 /2 is 2 1/2.Then 2 1/2 /2 is 1 1/2.Thats how I got 9

     
  • At 12:06 PM , Anonymous haseeb and dallas said...

    We think the answer is 7 1/2 because. We got this answer by thinking that the farmers brought 10 cows to the market.So the first person buys half of all the cows which equals 5 plus then he bought another 1/2 of a cow which equals 5 1/2.The second person buys half of of a cow and then another 1/2 which equals 6 1/2 then the 3 person buys 1/2 of a cow and then another 1/2 which equals 7 1/2

     
  • At 12:11 PM , Anonymous Jess said...

    This is the less confusing version that has more imagination: There's a farmer who went to market looking for a good deal on cows when he spots the farmer who's selling cows. This one looks easy to fool, he thought as he walked over. "I'll buy half your cows, and another man will come and pay for the last part." So the gullible seller agreed to this deal, and gave the man the cows. Soon another man came to buy cows. This must be the other man, thought the farmer."I'll buy half of these cows." replied the man. The farmer gave him the cows, but made him pay for the half. The man thought this strange, but paid for the 21/2 cows. Later, a third man came to buy. He had trouble deciding between a few cows, so, he decided only to buy half,but causually take the rest. So in plain view of the gullible farmer, he led all 11/2 cows he didn't buy away.

     
  • At 12:23 PM , Anonymous Anonymous said...

    I think the answer is 7 because 7 divided in half is 3 and 1/2 and 3 and 1/2 is 1 and a 1/2. The Half means that 2 people split the cost of one of the cows fifty-fifty.

    A.J.

     
  • At 12:25 PM , Anonymous Jess said...

    P.S. the total is 9 cows from the story.

     
  • At 12:28 PM , Anonymous Bridget said...

    I overheard Malcolm And Sandeep talking about how there was one cow. I'm sorry if this is a mistake, but it says that Mr.Haney brought his cowS to the market.

     
  • At 12:38 PM , Anonymous Bridget who is angry said...

    Well, first off, we don't know how many cows that the farmer started with (I had to read over it several times). And then I noticed that at the bottom, the question. So I added all of the whole cows and half cows together, because we need to know the total from before everyone bought the cows. It says that the third buyer buys the remaining cows, so there are none left. First, I decided to add together all of the halfs.I got 1 1/2. Since all three buyers bought whole cows, I looked at that. Well, I couldn't really figure out it like that, so I decided to experiment with numbers. I'll start with four, since it is the smallest even number bigger than two, and if the buyers bought that much, there wouldn't be less than 3 or 4. This will be continued because Haseeb is interupting my thinking.

     
  • At 1:23 PM , Anonymous Sandeep, Malcolm and Skyler said...

    Our answer is 3 and 5/8. How I got that was at first I left out the words "the first buyer buys half of the farmers cows" The I left in the part "plus 1/2 a cow". After that they said the second buyer half of the remaining which was 1/2. (The one half is when they said plus 1/2.)The half of 1/2 is 1/4. Then I added one half plus one half which is 1. Then the third buyer came and bought 1/2 of that which was which is 1/2 because it was 1/2 of 1 whole. Then they said plus 1/2, so I did 1/2 plus 1/2 which is 1 again. Then because of that I started all over and thought that the farmer brought 2 cows to the market. Then I restarted and they said the first farmer bought 1 cow because 1/2 of 2 is 1. Then plus 1/2 which is 1 and 1/2. Then the second buyer came and took half the remaining which 1/2 and like I said before 1/2 of 1/2 if 1/4. Then I did plus 1/2 and did 1/4 plus 1/2 and got 3/4. Then I did 1/2 of 1/4 and got 1/8. Then after I added 4/8 to it and got 5/8. Then they said each buyer bought 1 whole cow. Sp there were 3 buyer and I added 3 wholes plus 5/8 and got 3 and 5/8. So thats the answer.

     
  • At 2:06 PM , Anonymous Bridget who is no longer angry said...

    CONTINUED.............

    So, I will experiment with 7.(But just to explain why I am doing 7, I heard many finished people say that it was between 7 and 9.) I have to find half of 7(3 1/2), and then take half of the remaining 3 1/2(1 3/4), and then take half of the remaining 1 3/4(0.8), and then I add 1 1/2. (I add 1 1/2 because there are three halves, and added together they are 1 1/2.)The answer is 2 3/10). I think that the answer is way, but not too much over 7. 9 is my final answer.

     
  • At 3:29 PM , Anonymous Esha said...

    Well this problem is very tricky.
    For all the work i have done in the classroom i know the answer is less than ten & has to be higher than two..i think the answer is 8.5 dived by 2 =4.5that divided by to =2 then that divided by two eguals=1 plus 1.5 does not equal zero.so thats the problem.
    Mr.Stuart how can u figure it out so quickly.Well i will see when i figure out the answer.The problem is probaly really hard but the answer may be simple.

     
  • At 3:39 PM , Anonymous Anonymous said...

    from summer

    The farmer does not sell all his cows because the last buyer onley bought half of the cows remaning so the answer can be any thing as long as you do
    ( a * 2 * 2 * 2 * 2 + 1.5 + b )
    The person who was right eather did this or just guessed.

     
  • At 4:45 PM , Anonymous Mahrukh Habib said...

    This is quite confusing but here is my answer.
    Well I basically started mismatched.
    Like at the end I knew the last buyer bought 1 cow home since obviously he bought the remaining, but in the end there were not any cows left. I got confused but remembered that the last buyer also adds a half. So he bought 1 home all together.
    That also gave me the conclusion that the secound buyer left one.
    Then I suddenly thought of 7 cows.
    Half of seven is 3.5 cows plus a half is 4 cows thats what the first farmer took. But I needed to count the REMAINING so 3 were left over.
    The secound buyer came and took half of 3, which is 1.5. Then he took a half more. Which, like I said, left the last buyer with 1 cow. The last buyer took half of the cow and added a half.
    That is my final answer, It makes sense to me.
    From,
    Mahrukh!

     
  • At 5:59 PM , Anonymous mark said...

    I think the answer is 12 because two divided by 12 3 times equals 1.5 so I added 1 and a half of a cow and 1.5 + 1.5 = 3 cows per each person.

     
  • At 7:37 PM , Anonymous Esha said...

    continued from esha
    now i think it is 9
    will explain in class

     
  • At 7:47 PM , Anonymous Belle said...

    I think that the one and only answer is 12, because you divide 12 by 2 three times which equals 1.5, minus 1.5 = 0! I know that everyone mostly thinks that you have to add 1.5 but I subtracted it, because it says plus and that is the main definition for and, so you can just say '' the first buyer bought half of the amount of cows, AND half of a cow. So that probably has confused everyone. The problem was a great thinking problem and it helped me think! Thank You Mr. Stuart and Mr. Haney for showing the class this great thinking problem.
    From,
    Belle

     
  • At 8:03 PM , Anonymous Anonymous said...

    From: Wintwin
    We are absolutely sure that the correct the answer to this crazy cow problem is 7 and we don't need you to tell us were right, mathamaticly 7 fits perfictly. Here's why:
    There's 7 cows. The first farmer buys half the total cows and 1 extra half a cow equaling(4)total cows bought, now there's 3 cows left, the 2nd farmer buys 1/2 of them plus 1 extra half a cow equaling 2 total cows bought, now there is only 1 cow left, the 3rd farmer buys half of that cow plus 1 extra half a cow equaling 1 total cow bought. Leaving 1 very sad farmer who no longer has any cows left! LoL

     
  • At 8:41 PM , Anonymous zak said...

    I think it's 5 cows because the 1st buyer bought 2 and a half and the 2nd buyer bought 1 and a half and my MOM thought that the first and seconed buyers share a cow for the halfs and the 3rd and last buyer must have bought 1/2 and a 1/2 that equals 1 whole cow so thier were 5 cows!(I hope)Holy cow that was hard.

     
  • At 9:10 PM , Anonymous ryan said...

    Th answer is 1 cow!!!! because 1 is the only number that you can divide in half then add half bnd it keeps eing the same number.

     
  • At 7:25 AM , Anonymous ryan said...

    well, 1 is a god answer, but its not th right one. The real answer is 7 because 1 guy bought 3.5 cows + .5 cow = 4 cows. 3 cows left over. 2 guy bought half of those 3 = 1.5 + .5 + 2 cows. 1 left over 3 guy took .5 cow + .5 cow = 1 cow. 4+3+1 = 7 cows!!!!!! thanks for not letting my dad, big brother and me sleep!

     
  • At 7:25 AM , Anonymous ryan said...

    well, 1 is a god answer, but its not th right one. The real answer is 7 because 1 guy bought 3.5 cows + .5 cow = 4 cows. 3 cows left over. 2 guy bought half of those 3 = 1.5 + .5 + 2 cows. 1 left over 3 guy took .5 cow + .5 cow = 1 cow. 4+3+1 = 7 cows!!!!!! thanks for not letting my dad, big brother and me sleep!

     
  • At 8:27 AM , Anonymous Anton, Y. said...

    My answer would be 7 and a half because, every byer bought a half, and there were three, that makes 1 and a half but where did I get the other 6 hre is how: 6 is the only number when a half can be taken away the one more half and zero is what is going to be left.

     
  • At 9:13 AM , Anonymous niko said...

    I think he sold 3 5/8 the first buyer bought 1.75 which left 1.75 then the second buyer bought 0.86 then 0.50 so he bought 1.36 then the third buyer buys 1/2 or 0.5 which leaves 0.86 then half is 0.43 in total he bought 0.93 and thats how i got 3 5/8

     
  • At 5:29 PM , Anonymous briana said...

    its 7 because 1 guy bought 3.5 cows + .5 cow = 4 cows. 3 cows left over. 2 guy bought half of those 3 = 1.5 + .5 + 2 cows. 1 left over 3 guy took .5 cow + .5 cow = 1 cow. 4+3+1 = 7 cows

     
  • At 11:10 AM , Anonymous Derrick, Drew, Shelby, Gustavo, and Mr. Graham said...

    The WHS Calculus Class figured it out. It has to be 7. The first man bought half of the cows, which would be 3 1/2 cows plus 1/2 a cow which would make his total 4. The second man bought half of the remaining 3 cows, which would be 1 1/2 cows plus half a cow which would be 2 cows. The third man bought half of the remaining 1 cow, which would be 1/2 a cow plus half a cow which would be the remaining cow. -WHS CLASS OF 2009 CALCULUS CLASS

     

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