bonanova
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Everything posted by bonanova
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[spoiler= ]Four and a thumb?
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A huge bin contains distinctly numbered balls, and you choose two of them at random. I give you 2 to 1 odds that the numbers will be relatively prime. For example, You pick 6 and 13. I win $1. You pick 5 and 25. You win $2. Do you take the bet?
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Squares packed in triangluar boxes
bonanova replied to bonanova's question in New Logic/Math Puzzles
Here is a plot of the fractional area of the two squares. Fraction of triangle occupied by the two squares as a function of theta.
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Squares packed in triangluar boxes
bonanova replied to bonanova's question in New Logic/Math Puzzles
I had forgotten that plasmid published these same figures, that I just made. FWIW I'll post them.
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What is the likelihood of meeting in your lifetime someone having an above average number of arms? virtually impossible unlikely fifty-fifty fairly likely virtually certain
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I'm thinking of how to fill up the entire angle A in k-man's drawing. The reflex interior angle would have to approach 180 degrees to do that. That demands an infinite number of bents, whose angles approach 180 degrees as a limit. The requirement of an infinite number of bents contradicts the terms of the OP. Q. E. D.
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See post #4
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There is also a $10 gold piece. Although it's no longer minted, it's legal tender.
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Alternative answer is more than that.
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What's the largest number of U.S. coins ...
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What's the largest number of U.S. coins you can have without having even change for a dollar?
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A clock is observed. The hour hand is exactly at a minute mark, and the minute hand is six minutes ahead of it. Later, the clock is observed again. This time, the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it. How much time elapsed between the first and second observations?
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Agree. My post was aimed at proving an increased travel time. kman gave the best analysis.
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The 2/5-3/5 <==> 1/19 case probably admits to this proof as well. There would be 18 similar triangles instead of 6.
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@ unreality. LTNS. Nice to see you again.
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Two cents: do the same number of equally likely results round to each of the numbers in the desired range?
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I expect not, or it would not be a good puzzle, just a lengthy calculation. That said, I think we're all waiting for the arrival of an AHA! moment ...
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A very, very cool puzzle, indeed.
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A rough sketch for 1:2 split rules that out. Since 1/19 is the result for a 2:3 split, maybe there's a slip in how the ratio was used in the calculations. Try using a 1:1 ratio, and see if that calculates 0 area. You've done more analysis than I have.
