<p>There are 6 red, 6 brown, 6 yellow, and 6 gray scarves packaged in 24 identical, unmarked boxes, 1 scarf per box. What is the lease number of boxes that must be selected in order to be sure that among the boxes selected 3 or more contain scarves of the same color?</p>
<p>Any help? </p>
<p>I don't have the answer sorry, please explain this if you figure it out.</p>
<p>Thanks</p>
<p>Answer: 13 boxes. For this situation, you have you count out all scenarios. Best scenario: You open up three consecutive boxes and manage to end up with three different colors. However, the problem asks for a complete GUARANTEE of the fact that you will have three different colors therefore you need to take into consider the worst case scenario.
Worst case scenario: you open up 12 boxes and discover that you have 6 red and 6 brown scar(ves?). Therefore, you have to open one more to GUARANTEE the fact that you have three different colors. Hope that makes sense - I'm not so great at explaining mathematical concepts.</p>
<p>oops, forgot to mention earlier</p>
<p>the choices are </p>
<p>a. 3
b. 6
c. 7
d. 8
e. 9</p>
<p>sorry stockguru92...heh...you wrote that big explanation for nothing :(
And I think you read the problem wrong: it asks for 3 of the SAME color, not different color.</p>
<p>I've been on this problem for the last half an hour, still cant figure it out...argh.</p>
<p>help...</p>
<p>shud be 18 =s</p>
<p>where is this problem from?</p>
<p>Does stuff like this actually come on the SAT? :S</p>
<p>A similar question came on the SAT Math level 2 in december....</p>
<p>answer is 9 i believe cause you could open a red, gray, brown yellow ,red brown, yellow gray then a red either way by 9 you are going to know that you have 3 boxes of the same color. i think thats right</p>
<p>I second dude83190. I also think I remember this question from BB. 9 must be correct answer!!!</p>
<p>what if u pick 6,6,6 and then 1?</p>
<p>what do you mean 6,6,6 and 1 ??</p>
<p>The answer is 9. It's a very simple question that appears to be difficult. Look at it this way:</p>
<p>You have:
6 red
6 brown
6 yellow
6 gray</p>
<p>Assume that we pick them out in the order shown. We first pick out red, then brown, then yellow, then gray. So we now have 4 boxes, and we can guarantee at least 1 box of a colour (remember, we are trying to get the best case scenario in which we can guarantee 3 of one of the colours). We then pick out another 4 in the same order - red, brown, yellow, then gray. We have now picked out 8 boxes, and we can guarantee that there will be at least 2 boxes containing the same colour. Now that we have 2 boxes of each colour, we only need one more box to guarantee 3 boxes of the same colour. No matter what colour it is, we can take it.</p>
<p>So we need 4+4+1=9 boxes to guarantee that there will be at least 3 boxes containing the same colour.</p>
<p>Why does this guarantee 3 boxes of a colour? We have considered the worst case scenario - where we picked up as few of each colour.</p>
<p>It's kind of hard to explain, so sorry if I've made it sound a bit confusing :/...</p>
<p>Thanks all</p>
<p>I worked this problem out with other people at school today and we came up with 9 like Sci-Fry.
lol, we used the same method that sci-fry did.</p>
<p>This problem is actually from the 6 SATs you get from CB's Online Course.
Test 6, Section 8, Problem 11.</p>
<p>I torrented these and I found the answers for tests 1-5 from someone else on this forum but no one had the answers to test 6...:(
If anyone has them, would you please kindly email them to me: <a href="mailto:shubham.gandhi@gmail.com">shubham.gandhi@gmail.com</a></p>
<p>Thank you</p>
<p>Sent you a PM Shubham</p>
<p>what if you pick all 6 red and then all 6 brown and then so on..</p>
<p>^ yes but it wouldn't guarantee that you have at least 3 of one colour</p>
<p>This is like a math question my math teacher gave me in 7th grade: you're in a dark room with a cabinet with 700 socks that are either blue or black, and you can't see which is which. What is the minimum amount of socks that you need to take to get a pair of the same color?</p>
<p>^ 3. Same method as this...</p>