Michigan Selectivity

Colleges and Universities A-Z University of Michigan
61

<p>no. 6 for horses. </p>

<p>loaf of bread.</p>

<p>1st day. Give him 1/7 of the bread (cut once)… he has 1/7
2nd day. Cut 2/7 of the bread, give to him and collect the 1/7 that he has (cut twice) … he has 2/7
3rd day. Give him the 1/7 of the bread he gave you back. he has 3/7 (no cuts)
4th day. Give him the remaining 4/7 of the bread. Recollect the 3/7 he already has. He has 4/7 (no cuts)
5th day. Give him the 1/7 of the bread. He has 5/7. (no cuts)
6th day. Give him the 2/7 of the bread and recollect the 1/7. (no cuts) He has 6/7
7th day. Give him the 1/7 of the bread. He has 7/7 = 1 (no cuts)</p>

62

<p>For the egg one, do I have to determine it by actually dropping the egg? Can’t you put some pressure on the egg which you can measure the amount of pressure that would break it, and then determine what floor that would be if you were to drop it off the floor. Or perhaps you could somehow compare the eggs to other eggs and use the other eggs to get an estimate of what floor you can drop them off.</p>

<p>That’s probably what I’d have to say if I were in that situation. I have no idea.</p>

<p>My guess is though is that you start at floor 1 and move up 3 each time? So you start at floor 1 and if it doesn’t break, floor 4. If it does break floor 2. If it does that’s the minimum, if not try floor 3. If it does break that’s the minimum, if not 4’s the minimum. But that’s 33 drops, so I don’t know. </p>

<p>For the horse races my guess is 9. You race them in sets of 5 at first. Take all the first place horses and race them. Take all the 2nd place horses and race them. Take all the 3rd place horses and race them. Take the top 3 1st place horses and the top 2nd place horse and the top 3rd place horse and race them.</p>

<p>Do I need to cut straight cuts on the bread? Can I cut in a curved way? If so I would cut it like this:</p>

<p><a href=“ImageShack - Best place for all of your image hosting and image sharing needs”>ImageShack - Best place for all of your image hosting and image sharing needs;

<p>Red being the cuts </p>

<hr>

<p>Edit: How does the horses work? Errr… and still the egg?</p>

63

<p>someone wanna explain to me why my method is wrong?</p>

<p>i can get it down to at most 5 values (96-100) within 10 steps in the worst case scenario (if it doesn’t break at the 95 story drop). Testing at 99 would disprove 100 if it breaks, testing at 97 and if it breaks, I test at 96 to see it’s 96 or 97 is the min. If it doesn’t break at 97, then test 98 to see if 98 or 99 is the min.</p>

<p>that’s 13 steps! oh god why</p>

<p>…must be missing something.</p>

64

<p>Pro, you can only break it twice…</p>

<p>“drop from 95, if it breaks, drop at 93, if breaks, drop at 91”</p>

<p>You’ve broken it twice before you can drop at 91.</p>

<p>19 drops would work if you dropped from intervals of 10, and then as soon as it broke went to the previous floor and started 1 up from it. The most being at floor 99 or 100 where you would have tried 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 (break), 91, 92, 93, 94, 95, 96, 97, 98, 99 (break or not). </p>

<p>In intervals of 11 you would go 11, 22, 33, 44, 55, 66, 77, 88, 99, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, which is also 19.</p>

<p>In intervals of 12 you would go 12, 24, 36, 48, 60, 72, 84, 96, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95 which is also 19.</p>

<p>In intervals of 9 you would go 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 91, 92, 93, 94, 95, 96, 97, 98 which is also 19. </p>

<p>Crazy!</p>

<p>Varying intervals?</p>

<p>15, 29, 42, 54, 65, 75, 84, 93, 100, 94, 95, 96, 97, 98, 99 if it breaks on the 99th floor that’s 15… Yay only 1 off.</p>

65

<p>I just failed so hard at reading comprehension.</p>

66

<p>If you’re guarinteed it’ll break from dropping at any height on the building you could just avoid dropping it at 100, and that would be 14. Other than that I don’t know.</p>

67

<p>I’m confused about the horse one. Just to race each horse once, you would have to do five heats. You could then race all the winners against each other, but a second or third place horse in one of the heats might have been faster than one of the other first place horses. Get what I’m saying? Personally, I got 12.</p>

68

<p>I can see 7 horse races by doing all the sets of 5, racing all the winners, taking the #2 and #3 winner and racing them with the 2nd and 3rd place in the race that had the #1 in in the winners race, and the 2nd place horse from the race that had the #2 horse. The top 2 of that race and the top of the winners race would be the top 3. </p>

<p>Still don’t see 6 though.</p>

69

<p>sorry i meant 7. I was racing to leave work. I was there since 5:30 am lol. So I miss-typed it. and your explanation is right. It’s not hard you just need to picture it in your head. </p>

<p>If you draw it out, it’s even easier to understand.</p>

70

<p>Ok. That makes sense.</p>

71

<p>Sorry, i forgot. the assumption is the egg has to break. So the last one of the interval is a special case of 99. If it doesnt break from 93-99, it has to be 100. so no need for 15.</p>

72

<p>I got 14, but I didn’t use equations (not explicitly anyways)…</p>

73

<p>I’m working on 3 eggs and 1000 floors, and so far I’ve figured out that 23 is the maximum, so I need to see how much lower I can go. It’s between 14 and 23</p>

74

<p>omg how did i not realize that…it’s a nested search… the answer should be 19…</p>

75

<p>that’s what i got too, although i don’t know what a nested search is.</p>

76

<p>

Undergraduate enrollment by geographical location (Fall 2007):
<a href=“http://www.ro.umich.edu/report/07fa115.pdf[/url]”>http://www.ro.umich.edu/report/07fa115.pdf&lt;/a&gt;&lt;/p&gt;

<p>Oakland … 4,895
Wayne … 2,581
Washtenaw … 1,982
Macomb … 972
Kent … 883
Genesee … 464
Kalamazoo … 486
Livington … 386</p>

<p>Total … 10,432 (75% of in-state enrollment)</p>

<p>

Not quite. Only 65% of the undergraduate student body is in-state.</p>

77

<p>“Not quite. Only 65% of the undergraduate student body is in-state.”</p>

<p>GoBlue, anything above 50%, is considered majority.</p>

78

<p>"Undergraduate enrollment by geographical location (Fall 2007):
<a href=“http://www.ro.umich.edu/report/07fa115.pdf[/url]”>http://www.ro.umich.edu/report/07fa115.pdf&lt;/a&gt;&lt;/p&gt;

<p>Oakland … 4,895
Wayne … 2,581
Washtenaw … 1,982
Macomb … 972
Kent … 883
Genesee … 464
Kalamazoo … 486
Livington … 386"</p>

<p>Interesting you didn’t mention that the majority of the list consists of double if not single digit numbers.</p>

79

<p>For the 3 eggs dropping 1000 stories I’m getting 22. What sequence gives you 19?</p>

80

<p>

This is in response to your claim that the top 10% number for Michigan is “less meaningful” because "the majority of the accepted students are in-state and most Michigan high schools are small.</p>

<p>I just proved to you that 84% of Michigan’s student body are NOT from SMALL Michigan high schools. Thus your claim that the top 10% figure is “less meaningful” is invalid. Surely people with your intelligent will understand that.</p>