Peace Of Mind
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Post by Peace Of Mind on Aug 5, 2013 13:22:36 GMT -5
Oh, you can "flip" me any time you'd like! Whatever floats your boat, I guess. LMAO!!! Virgillllll. You are going to hellllllll. Did Beer turn you down again? But that emote is awesome!
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Aug 5, 2013 13:28:38 GMT -5
We NEED that emot!! There must be room for it on the emot menu.
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Virgil Showlion
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Post by Virgil Showlion on Aug 5, 2013 13:30:43 GMT -5
Yeah, that's going to happen. To: admin, mods Subject: "Eff you" Smiley Hi Guys, Figured I should give you a heads up about this. I know we're riding on "respect your fellow posters" and "attack the argument, not the person" really hard, but Beer really wanted me to put it in. Cheers, Virgil
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Post by Deleted on Aug 5, 2013 13:32:25 GMT -5
Let me know if it will take a more "persuasive" argument!
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Peace Of Mind
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Post by Peace Of Mind on Aug 5, 2013 13:34:31 GMT -5
Yeah, that's going to happen. To: admin, mods Subject: "Eff you" Smiley Hi Guys, Figured I should give you a heads up about this. I know we're riding on "respect your fellow posters" and "attack the argument, not the person" really hard, but Beer really wanted me to put it in. Cheers, Virgil We are smart enough to know you were flipping beer and not flipping Beer off. I did add it to the wish list for shits and giggles and I know most of us would have fun with it amongst friends. But some times you never know who those "friends" are from year to year so I'm sure some would become all insulted over it. But I can still wish for it.
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Aug 5, 2013 13:34:50 GMT -5
It's really a matter of perspective what you interpret the emot doing. It also looks like it's ready to flick a fresh booger.
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Virgil Showlion
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Post by Virgil Showlion on Aug 5, 2013 13:55:27 GMT -5
It's really a matter of perspective what you interpret the emot doing. It also looks like it's ready to flick a fresh booger. Uh huh. Wait. I'm having another premonition. ... Reported User: ymcouponmom1 Reported Post:Reported By: couponsr4losers25 Report Reason: This is a personal attack against me. Delete it you mods, or there will be blood! Report Discussion:
mmhmm: I'll get it.
Scottish_Lassie: I think we should leave it be. She's saying "You and your Costco loving friends are nose-pickers," IMO.
mmhmm: Are you sure?
Scottish_Lassie: Yes. The little guy has a booger on his finger. False alarm.
Report archived.
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Virgil Showlion
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Post by Virgil Showlion on Jan 17, 2014 19:33:28 GMT -5
Problem 76 - Death by Canadian Taxes
You are a hardworking trucker that has to deliver a total of 1,800 eco-friendly push lawnmowers from a warehouse in Toronto to a store exactly 600 kilometers away in Sault Ste. Marie. Your rig can carry up to 600 lawnmowers at a time.
But Canada being the haven for idiotic self-defeating socialist policies that it is, the Canadian federal government has imposed a carbon tax of one lawnmower per kilometer traveled by any vehicle carrying one or more lawnmowers of any kind.
Given these circumstances, what is the greatest number of lawnmowers you can deliver to Sault Ste. Marie, and how do you do it?
(Note: You must travel through Canada. Attempting to cut through the US will cause your mowers to be seized at the border as WMDs and you'll rot away in Guantanamo for the remainder of your natural life.)
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The Captain
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Post by The Captain on Jan 17, 2014 19:38:03 GMT -5
I don't get it, if they are push lawnmowers there are no carbon emissions > Am I missing something? I know, get goats instead!
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Jan 17, 2014 19:42:35 GMT -5
A new BTOTD after 5½ months? Yay.
I'll have to rummage around now for my thinking-cap - I forget where I dropped it when the last one ended.
I haven't even read the puzzler yet.
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Jaguar
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Post by Jaguar on Jan 17, 2014 19:45:52 GMT -5
Answer : Virgil is doing his taxes and he's screwed royally.
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Jan 17, 2014 19:53:56 GMT -5
Three eco-friendly push-mowers will end up being delivered to Sault St Marie out of the 1800 total.
The first lawnmower (out of 1 truckload of 600 mowers) will have to be relinquished as payment for the carbon tax after 1 km has been traveled. And that will continue for the next 598 km - with giving up 1 lawnmower every km in taxes.
The final km driven will end at the destination (Sault St Marie) with one lawnmower left on the truck.
The trucker can then make the return trip back to Toronto carrying no cargo.
He then has to repeat the same route to SSM as before two more times - relinquishing 1 mower every km for 599 km. with the 2nd, and then 3rd and final mower being dropped off in Sault St Marie.
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Virgil Showlion
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Post by Virgil Showlion on Jan 17, 2014 20:06:22 GMT -5
Three eco-friendly push-mowers will end up being delivered to Sault St Marie out of the 1800 total.
The first lawnmower (out of 1 truckload of 600 mowers) will have to be relinquished as payment for the carbon tax after 1 km has been traveled. And that will continue for the next 598 km - with giving up 1 lawnmower every km in taxes.
The final km driven will end at the destination (Sault St Marie) with one lawnmower left on the truck.
The trucker can then make the return trip back to Toronto carrying no cargo.
He then has to repeat the same route to SSM as before two more times - relinquishing 1 mower every km for 599 km. with the 2nd, and then 3rd and final mower being dropped off in Sault St Marie. OK. So your strategy gets three mowers to the destination... although it would actually be zero since driving 600 mowers over 600 km would incur a tax of 600 mowers each time. Assume that even though you're at the destination with the last mower after you've traveled the last kilometer, the government is still going to confiscate it as payment for driving it that last kilometer. And at any rate, the best strategy is much better than 3 mowers. Put on your thinking caps again. The Canadian government is actually too dumb to recognize that. You see, the way things work in Canada is that some bureaucrat gets it into his/her head that ALL X = EVIL AND MUST BE TAXED, where X is an extremely broad category of good, like "lightbulbs" or "home insulation". The bureaucrats have absolutely no technical knowledge and don't bother differentiating between eco-friendly X and non-eco-friendly X. They just tax the snot out of everything indiscriminately, pocket their six-figure salaries, and go home each day secure in the knowledge that they've made the world a safer and less evil place. So the fact that push mowers make no emissions and levying carbon taxes on them is a stupid idea unfortunately doesn't mean that the Canadian government wouldn't leap at the opportunity to do so.
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Jan 17, 2014 20:10:33 GMT -5
And here I thought the carbon taxes were for the emissions from the delivery truck - not the lawn-mowers themselves. Silly me for thinking logically.
And to clarify my solution - I pictured the "tax collectors" stationed every km along the route - I assumed there wouldn't be one waiting at the entrance of the delivery point - which would be out of his/her jurisdiction.
I think my answer is more correct than you give it credit. So there.
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Virgil Showlion
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Post by Virgil Showlion on Jan 17, 2014 20:20:11 GMT -5
The way you envision it is fine. Just add another tax collector standing at the warehouse. Or imagine that one mower evaporates for every kilometer you drive. This isn't a lateral thinking problem with a trick solution. Although since it may not be obvious, I'll add that you may safely leave mowers at any intermediate waypoint and pick them up later. If you didn't have this ability, then the solution becomes trivial: no strategy exists that gets even one mower to the destination. I'm off for the weekend. But keep working on it. Fame and glory await the one who delivers the most mowers!
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Jan 17, 2014 20:48:30 GMT -5
The reasoning behind my "solution":
For the first km traveled from Point A (Toronto) to Point B (Sault St Marie), there are still 600 push-mowers on the truck at the checkpoint from factory to km #1. So that's basically a "free" km of travel before tax is imposed.
The driver is only taxed on the next 599 km. leaving 1 push-mower left on the truck at point of arrival.
That route gets traveled 2 more times bringing the total delivery of mowers to 3 at destination point out of a total of 1800.
I didn't skip a grade in school for nuthin'.
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Apple
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Post by Apple on Jan 17, 2014 21:33:38 GMT -5
He starts off with 600 mowers, drives half way, and loses 300 mowers. Heads back to pick up another 600, loses 300 the half way point. Loads original leftover 300 into the truck, drives the last 300. Loses 300, still has 300 left. That was only 1200 of the 1800 original mowers. If he went back for all 600, he'd lose them all. The best delivery would have multiple stop and unload points over the road. So he could drive 600 half way. Lose 300. Go back, pick up 600 more. Drive half way, lose 300. Go back and pick up 600 more. Drive half way, lose 300. At the half way point he has 900 mowers. Drive 600 another 150, lose 150, go back for 300. Drive 150, lose 150. Gather all 600 he has left, drive the final 150, lose 150, end with 350 mowers. He could just keep making stops to lose fewer mowers. Not the final number, but that's the process ETA: I may not have skipped a grade, but I could have. Instead, I took calculus when I was 16, and took advantage of all the higher math and science classes I could get for free/almost free while I was still in high school.
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spartan7886
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Post by spartan7886 on Jan 17, 2014 21:44:37 GMT -5
The trucker drives 200 km with the first load of 600 lawnmowers. Every km he pays a 1 lawnmower tax and drops 2 lawnmowers off, which nobody steals because Canadians are too polite. He drives the empty truck back to Toronto. There are now 400 lawnmowers on the side of the road.
The second load, the driver starts out with 600 lawnmowers. Every km of the first 200 he pays a 1 lawnmower tax and picks up one replacement lawnmower. Thus, he has 600 lawnmowers at 200 km and there are still 200 lawnmowers on the side of the road. For the next 300 km, he pays a 1 lawnmower tax and drops 1 lawnmower off. Thus, there are now 500 lawnmowers on the side of the road most of the way to Sault St Marie, greatly confusing the locals. He drives the empty truck back to Toronto.
The final load, the driver again starts out with 600 lawnmowers. Every km of the first 500 he pays a 1 lawnmower tax and picks up one replacement lawnmower. At 500 km, he still has 600 lawnmowers, but has run out of lawnmowers on the side of the road. Thus, he must pay the tax on the final 100 km with no replacements, arriving in Sault St Marie with 500 lawnmowers.
Edit: The driver could also leave all the replacement mowers at the end of each of the first two loads like Apple would do. The answer comes out the same as long as the driver completely fills up his truck whenever he reaches a stash of lawnmowers.
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Jan 17, 2014 22:33:46 GMT -5
The simplest solution to getting all 1800 mowers to the destination point and avoid the heavy fuel emission taxes on the highway route, would be to transport all 1800 units in a rail car - or air transport from Point A to Point B. Then delivery via truck would only be to/from air or rail terminal to final destination point.
(I think too far outside the box).
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Jaguar
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Post by Jaguar on Jan 17, 2014 22:59:43 GMT -5
The simplest solution to getting all 1800 mowers to the destination point and avoid the heavy fuel emission taxes on the highway route, would be to transport all 1800 units in a rail car - or air transport from Point A to Point B. Then delivery via truck would only be to/from air or rail terminal to final destination point.
(I think too far outside the box).
No I think the box closed it's doors permanently on you.
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Apple
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Post by Apple on Jan 18, 2014 0:37:46 GMT -5
trip 1 600-200=400 trip 2 600-200=400 trip 3 600-200=400
total 1200 mowers at 200km
trip 4 600-200=400 mowers trip 5 600-200=400 mowers
total 800 mowers at 400 km
trip 6 600-100=500 mowers trip 7 200-100=100 mowers
600 mowers at 500km
trip 8 lose 100 mowers the last 100 km
arrive with 500 mowers
(same final answer as spartan's, different method)
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Virgil Showlion
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Post by Virgil Showlion on Jan 19, 2014 8:38:17 GMT -5
Spartan and apple both present correct (optimal) strategies! And indeed, getting 500 mowers to the destination is the best result that can be achieved. The 'official' solution is apple's, since it involves the least number of drop-off/pick-ups, but in fact any solution (Rachets' being a particularly innovative example) that moves the full inventory of apples to the two waypoints (200 km, 500 km) is also an optimal strategy given the problem statement. SL also gets a 'like' for her outside-the-box solution.
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Virgil Showlion
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Post by Virgil Showlion on Jan 22, 2014 20:13:41 GMT -5
Problem 77 - The Physics TrifectaThree physics problems to tickle the mind and dazzle the senses! "Scientific genius" props to all posters who submit correct answers to any of the problems. If you know the answer to more than one, please answer only one to give other posters a chance. And of course: NO GOOGLING. If you Google the answer to a problem, you void your right to submit an answer in this thread, on your honour. Problem 1 - The Blue-Yellow ParadoxJim and Nancy are arguing about colour theory. Jim is a graphic designer and claims that Blue + Yellow = White. And indeed, if Jim mixes blue and yellow on his computer software, the light from the blue pixels combines with the light of the yellow pixels to make pure white pixels. He also has a handy colour wheel showing him that the overlap of blue and yellow is white. Nancy is a painter and claims that Blue + Yellow = Green. After all, if she mixes her blue paint with her yellow paint, she gets green paint. Every painter knows this. Nancy also has her own handy colour wheel showing that the overlap of blue and yellow is green, which basically every kid has known from grade school. Both Jim and Nancy are actually correct, but why? How can both answers be correct, and what makes all the difference? Problem 2 - The Cork and the Pail
The cork from a wine bottle is held by a robotic clamp at the bottom of a pail of water and released the moment the bucket is dropped off the side of a tall building. What will happen to the cork during the fall? Will it float to the top of the pail normally, slower than normal, or faster than normal? And why? Assume that there is no air resistance to slow the pail down as it falls. Problem 3 - Balance a Broom
Suppose you balanced a broom horizontally on your finger, so that your finger is exactly on the broom's center of gravity. You mark the spot and then cut the broom in two there, giving you a long piece and a short piece. The long piece consists of most of the handle, and the short piece consists of the bristle end a small part of the handle. What will happen if you weigh both pieces? Will the short piece weigh more than the long piece, will the long piece weigh more than the short piece, or will both pieces have exactly the same weight?
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Jaguar
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Post by Jaguar on Jan 22, 2014 21:15:18 GMT -5
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Apple
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Post by Apple on Jan 22, 2014 21:26:21 GMT -5
Problem #1 has to do with "light emitting" and "light absorbing". The paint absorbs light, whatever light reflects back is the color you see. Since a computer screen emits light, it has to combine the right waves to give you the color you need to see.
Oversimplified, but remembered from my computer programming classes.
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Jan 22, 2014 21:30:21 GMT -5
In Problem #1, All colors combined, in terms of "light" (or pixels) produce white - the center of chart #1.
If you're combining paints, for example - then chart #2 (blue & yellow) produces green.
I'm not even going to try & tackled Problem #2.
In Problem #3, yes each piece of the broom will have equal weight - IF the cut is accurate.
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Virgil Showlion
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Post by Virgil Showlion on Jan 22, 2014 22:26:53 GMT -5
Problem #1 has to do with "light emitting" and "light absorbing". The paint absorbs light, whatever light reflects back is the color you see. Since a computer screen emits light, it has to combine the right waves to give you the color you need to see. Oversimplified, but remembered from my computer programming classes. Yes, this is essentially the correct explanation. Yellow is produced by the superposition of red and green light. Superimposing blue with yellow yields full spectrum (red + green + blue = white) light. Superposition of light is what is called "additive" colour theory. As you indicate, paints and pigments absorb light. A paint appears light blue (approaching teal) when it absorbs red wavelengths, reflecting the green and blue. A paint appears yellow when it absorbs blue wavelengths, reflecting the red and the green. A mixture of the two pigments will absorb much of the red and blue wavelengths, reflecting predominantly the green. The exact shade, of course, depends on the shade of blue, the shade of yellow, and the ratio in which the two are mixed. Superposition of the absorptive properties of pigments is what is called "subtractive" colour theory, since it's the arithmetic of removing wavelengths rather than adding them.
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Lizard King
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Post by Lizard King on Jan 23, 2014 9:18:12 GMT -5
Hmm.
Problem 3 is about moments. The broom balances when the moment of the long piece and the moment of the short piece about the pivot of your finger balance out. The moment is a product of the force on either side of the pivot (in this case, the downward force of the weight of the broom on either side) and the distance from the pivot to the point where that is applied.
If our broom were a homogenous beam, it would achieve balance when the pivot were exactly halfway along the beam - because the weight of the beam on either side of the pivot would be the same, and would be applied at the same distance from the pivot, to create cancelling clockwise and anticlockwise moments.
We know, however, that the pivot here will have to be much closer to the head of the broom than the center of the shaft, because most of the weight is concentrated in the head of the broom. The fact that the distances from the pivot to the center of mass on either side of the pivot are unequal tells us that the masses on either side must also be unequal, and hence the weights of the two pieces are likewise unequal.
If we denote the weight of the short piece W, and that of the long piece w; and the distance from the pivot to the center of mass of the short piece d, and that of the long piece D; we can write:
W x d = w x D (this represents the balance of the clockwise and anticlockwise moments)
Then it follows trivially that W = D/d x w, i.e. W > w since D > d.
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Post by Deleted on Jan 23, 2014 9:18:47 GMT -5
I am surprised that one of our resident Oenophiles hasn't chimed in on this one yet! My guess is that the cork would float normally because the entire system is moving at the same rate of speed, but I have been known to be wrong in the past.
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Lizard King
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Post by Lizard King on Jan 23, 2014 9:26:26 GMT -5
Problem 2 is a little bit like the old 'elevator in free fall' thingy.
The cork is naturally buoyant. With the pail at rest, the forces acting on it are the upward force of its buoyancy, and the downward force of the clamp. If we release the clamp, the cork moves upward and floats to the surface where it comes to rest.
How does this picture change if the whole pail is falling?
If there were no cork - there were just a pail of water - and we dropped the pail from an arbitrary height, would we expect the water to remain in the pail? I think we would, but there'd be some loss on the way down, even assuming the pail stayed perfectly upright. The pail and the water are not homogenous - just as you feel a force pushing you back in your seat when you accelerate in a car, the water is going to experience a force opposing the free fall of the pail.
I don't think this will effect the buoyancy of the cork, however; what it might effect is the total distance the cork has to travel in order to reach the surface of the water. I'm deeply unconvinced by this suggestion, but I think the cork effectively floats slower because it has effectively further to go - the distance from the bottom of the pail to the surface of the water is greater with the pail in freefall than with the pail at rest.
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