bonanova
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Everything posted by bonanova
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Yup.
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You're correct about the wording of the OP, but no trick intended. With all the correct assumptions, tho, you're missing a few encounters.
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Sorry if the OP is confusing on the overlap / overhang question. I'll be more specific here. Plates are allowed to overhang the table, just so long as the center of the plate lies on the table. That is true for the original 12 plate configuration as well as the completely covering case. That is, no plate can be added without overlapping another plate, even tho it might overhang the table. This means your table could shrink by a plate radius on each edge.
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Every day at noon, a Greyhound tour bus leaves New York for San Francisco, and another [Greyhound] bus leaves SF for NY. The cross-country trip takes 168 hours [7 days and 7 nights] and follows Interstate 80 from end to end [George Washington Bridge to Oakland Bay Bridge.] How many Greyhounds [buses] will the bus leaving New York today encounter on its trip to San Francisco?
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What PT is saying is that you've drawn the plates closer together than the OP says they have to be. Or, that the OP allows the table to be bigger than you've drawn it. That is, if you want to prove that a certain number of plates is enough to cover a table [any table] consistent with the OP, then you have to deal with the most difficult case that the OP permits. Putting it another way, if N plates cover the table you drew, but won't cover a bigger table that is still consistent with the OP, then you haven't proved that N guarantees coverage. That is, a counter-example [bigger table] exists for which N fails. But if N suffices for the worst-case [largest possible] table, then you've proved that N will succeed for any table. The OP has the word ensure in it.
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Actually, only when it's not rounded to the nearest anything. Consider: 1/3 = .33 .... That equality is true only when the 3's go on indefinitely. If they're truncated [terminated] after n decimal places, the equality fails. Now multiply both sides by 3: 1 = .99 ....
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Well you [both] are clearly in the ballpark. So let's take that number for now: How do we know that number is certain to cover the table. How do we know a lower number might not cover the table.
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Nope. I see your approach, but recall we have to completely cover the table. Because the plates are circular, that means they will have to overlap. And we need a proof of sorts, and spoilers, please.
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Your disqualification might be premature. Give it a little more thought. The dessert plate thing was triggered by some great strawberry short cake I had yesterday during the super bowl....
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Prof T has come in with the lowest estimate to date. Can anyone prove that fewer plates will do the job?
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You're probably right about my knowledge of plates. If it will help, I'll say they are dinner plates. But if all the plates you named can be like what I described, then it would be fair to assume the plates are of any of those types. You know what? Now that I'm thinking about food, let's say they are dessert plates. I suppose it would help to know what type of table [kitchen, dining room, banquet, TV tray] is involved, also. But I'll leave that as part of the puzzle. Cute avitar, btw.
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Right.
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OK on Abs. Max takes two arguments....
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Bingo.
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Clarification... By "cover" we mean that the table does not show at all. Overlap therefore is not only allowed, it's needed.
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Circular, flat.
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Coffee and donut next visit to NY for the lowest provable number. It's the proof that's so cool. We're still high on the number, btw.
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You all got it...
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Rectangle. I bet you can prove that many fewer will do the job.
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Take the 9 non-0 digits in the following order: 7 o 5 o 3 o 8 o 1 o 6 o 4 o 2 o 9 Replace each "o" with either "+" or "x" and evaluate left to right. What the smallest result?
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For real numbers x, absolute value and maximum have the following meanings: Abs(x) is just the value of x without regard for sign: Abs(-3.3) = Abs(3.3) = 3.3 Max(x1, x2) is the larger of x1 and x2: Max(-9.2, 5.7) = Max(4.2, 5.7) = 5.7 Just for fun, express Abs in terms of Max. For a bit of a challenge, express Max in terms of Abs. Have fun.
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Hats on a death row!! One of my favorites puzzles!
bonanova replied to roolstar's question in New Logic/Math Puzzles
The riddle asks that no information be passed other than the word BLACK or RED. It's fun to think of ways to pass other information, but all that does is get everyone killed. -
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Corollaries, from my youth ... I'm sure there are others.
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Hi Bailey, and welcome to the Den. Great puzzle, but it has been posted here several times already. Please read the "before posting" blurb about searching for puzzles already on the forum.