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HoustonHokie

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Everything posted by HoustonHokie

  1. Re-reading the question, I see that 12 plates already cover the table... I was thinking this was like the last one, and the 12 went along one axis. In that case, I can do it with... edit: wait, reading the puzzle again, I think I see what you are looking for is a general solution no matter the what the dimensions are. I'll keep looking
  2. Rectangle or square? If rectangle, I might need another dimension to get the answer. If square,
  3. Actually, that's what they told you to begin with... and then you had to go and be all irate and stuff
  4. In January every year, Cub Scout Pack 123 holds its annual Pinewood Derby competition. The competition (for those who've never seen a Pinewood Derby) is held to determine which Cub Scout (and/or his dad ) can build the fastest car from a block of wood and some standard wheels. At Cub Scout Pack 123, the Derby is held on a track with 6 lanes. Cars race against one another in heats, and the competition is set up so that each car gets one run in each lane of the track. The car with the lowest average time across all lanes is declared the winner. Prizes are given to the top 3 cars in each Den and the top 3 overall. For many years, the competition went on and was running relatively smoothly, except for the normal little hiccups that seem to happen at every Derby. But two years ago, the number of cars entered in the race ballooned. The Derby, which used to take 2 hours to run, dragged on for 4 hours that year. And if you've ever been in a room with a whole bunch of bored Cub Scouts who don't have anything to do except wait for their car to make a trip down the track -- well, let's just say they don't have the greatest attention span in the world, and general chaos ensued. By the time the exhausted Cub Master left the Derby grounds that afternoon, he was vowing that next year would be different. And it was. The Derby Committee met, and they decided to adopt new rules for the next year. Instead of running all cars in all 6 lanes, each car would race just twice. The lane assignments would be random so that no one would claim bias or preferential treatment. And, as in years past, the winners would be the car with the lowest average times. So, last year, the Derby was held with the new rules in place. And the competition, even though it had more cars than the previous year, took less time and seemed to go more smoothly. That is, until the winners were announced. It seems that Lane 4 had more winners than all the other lanes put together. One particularly irate parent complained that his son, whose car raced only in Lanes 2 & 6, was only 0.01 seconds behind the winners in Lane 4. They claimed that if their son's car had raced in Lane 4, it would have placed among the winners. So the Derby Committee had a new problem: how to ensure a fair race with the minimum number of heats. As you are the aforementioned irate parent, the Committee has come to you for suggestions of new rules to solve their problem. Begrudgingly, you accept their offer. You look into the race results from the past couple of years, and you make some findings as follows: Although Lane 4 has the most winners, Lanes 1 & 2 also have a significant amount of fast times. Each lane of the track produces the fastest time for some cars, but not for others. Times across all lanes generally do not vary by more than 5% for invidual cars. In years past, there was an average of 60 cars entered in the Derby from 6 Dens (10 Cub Souts in each Den). In the last two years, there was an average of 120 cars entered in the Derby from 10 Dens (12 Cub Scouts in each Den). It is unknown how many Dens or cars will be in the competition this year. The Committee wants to keep the award structure in place as it has been in the past, with prizes to the top 3 cars in each Den and the top 3 overall. What do you tell the Committee?
  5. In which case I think he should owe for the 40 * 17 = 680 gallons he diluted! Don't give me that watered down stuff...
  6. YEESSSSS!!!! I'm going to Disneyworld! Or something like that... Got to read the fine print
  7. Couldn't upload the images here, so I've uploaded the images there: Blocks 1 Blocks 2
  8. Not sure about that scaffolding pattern, but I found a 1, 4, 9, 16 pattern that works. I also found the 1, 4, 9, 12 pattern that you saw. Here's the formulae: If L is the layer, the number of scaffolding blocks on that layer is 1. (L-3)2 2. L even: (L-3)2 L odd: [(L-2)2 - 1] / 2 I've taken both out to 9 layers deep and they work. I just can't get my pictures to upload because I've blown my attachment space . Here's how I would write a description for each: 1. Solid scaffolding except the diagonals are removed. If L is odd, you will get a perfect X shaped diagonal. If L is even, the center of the diagonal will be 2x2 instead of 1x1. In this case, add a central block rotated 45 degrees. When viewed from below, it looks like you're creating 4 small triangular pyramids inside the larger square pyramid. 2. Exactly the same as #1 on the even layers. For the odd layers, use a checkerboard pattern. I think the professor had pattern #1 in mind when he wrote the OP because 1300 blocks makes exactly 16 layers that way. But pattern #2 is more efficient and requires only 1160 for 16 layers and can accomplish 17 layers with 1336 blocks. We may be able to improve on this if we can figure out a good checkerboard pattern for the even layers. I'll see if I can improve the efficiency of my graphics and may post my pictures later . It may be good to define exactly what "stable" is for this exercise. I've taken it to mean that one of the following conditions is true: 1. a block is completed supported from below 2. a block has one side completed supported* and at least one point on the opposite side supported 3. a block has two adjacent sides completely supported* * when I refer to a side as completely supported, I mean the actual edge plus some offset (generally half the width of the block, but I suppose it could be less)
  9. You're right. I was in the middle of drawing it out when I saw your post. I had come to the same conclusion and was trying to see if there was any way to salvage my idea. No such luck so far
  10. IMHO, it would be splitting hairs to say that this is non-calculus. You have done all the work that forms the very definition of an integral without actually using the established calculus "rules" for performing integration of the function. One way to define the integral of a function from f(x=a) to f(x=b) is the area between the function and the x-axis between x=a and x=b. In calculus, you prove this by taking the limit of the area under the function as the difference between a & b becomes infinitesimally small. You've done exactly that by increasing the number of iterations in your program. In order to get the "exact" answer, your program would have to have infinite iterations. Of course, you can see what the answer is tending towards with a finite number of iterations and make the logical leap to that solution, but to get the exact answer I think you need the calculus. You didn't come up with the integral function so the area could be directly evaluated, and maybe that leaves you in the non-calculus realm -- but just barely. The closer you get to the exact solution, the more you're doing calculus
  11. [spoiler='10 letters']a am tam tame tamed teamed steamed streamed streambed streambeds a an ane anes sanes stanes stances stanches staunches staunchest a an tan tang stang strang strange stranger strangers stranglers n in pin ping oping coping comping compting competing completing I must confess I don't know the definitions of all of these, but they all appear in the Official Scrabble Players Dictionary, so they must be real words, right? And I think this is as far as we can go - I can't make any of these into 11 letter words.
  12. HoustonHokie

    What you're driving at is how I know that the radius point of the circle is exactly 1/2 the base length from the base. Here's the explanation:
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