A man starts walking up a mountain on a well worn path at 7:00AM. He reaches the top at nightfall and spends the night in a Cabin. The next day, he picks up a large rock as a momento and begins walking down at 7:00AM. Is there a time when was in the exact same location on the path at the exact same moment of the day on both days?Doug wrote: ↑Thu Nov 18, 2021 4:25 pm I heard an amazing math "trivia" question yesterday
A basketball player has a free-throw percentage of less than 75 percent early in the season.
By season's end, his free-throw percentage has risen to above 75 percent.
Is it necessarily true that his free-throw percentage was ever exactly 75 percent?
Doug's Fiendish Trick Trivia Questions
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Re: Doug's Fiendish Trick Trivia Questions
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Re: Doug's Fiendish Trick Trivia Questions
Crunchums wrote: ↑Thu Nov 18, 2021 5:21 pmprobably people understand this already, but just in case:Doug wrote: Of course this is exactly the issue
S(n)/n < 3/4 < (S(n) + 1)/(n + 1)
has solutions for n, but none of them are integers. Isn't that neat
when I said "is there a rational number a/b..." I was being imprecise; what I meant was "are there rational numbers a and b such that a/b..."
Rylinks jumped on my imprecision as an opportunity for trolling (or at least that was my read of his post)
You were being quite precise, just not in the way you wanted.
Re: Doug's Fiendish Trick Trivia Questions
Is it nightfall when he arrives back at the bottomgroff_enthusiast wrote: ↑Mon Nov 22, 2021 3:23 pmA man starts walking up a mountain on a well worn path at 7:00AM. He reaches the top at nightfall and spends the night in a Cabin. The next day, he picks up a large rock as a momento and begins walking down at 7:00AM. Is there a time when was in the exact same location on the path at the exact same moment of the day on both days?Doug wrote: ↑Thu Nov 18, 2021 4:25 pm I heard an amazing math "trivia" question yesterday
A basketball player has a free-throw percentage of less than 75 percent early in the season.
By season's end, his free-throw percentage has risen to above 75 percent.
Is it necessarily true that his free-throw percentage was ever exactly 75 percent?
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Re: Doug's Fiendish Trick Trivia Questions
Maybe a little before, or a little after, the rock was so heavy it's hard to rememberDoug wrote: ↑Mon Nov 22, 2021 3:31 pmIs it nightfall when he arrives back at the bottomgroff_enthusiast wrote: ↑Mon Nov 22, 2021 3:23 pmA man starts walking up a mountain on a well worn path at 7:00AM. He reaches the top at nightfall and spends the night in a Cabin. The next day, he picks up a large rock as a momento and begins walking down at 7:00AM. Is there a time when was in the exact same location on the path at the exact same moment of the day on both days?Doug wrote: ↑Thu Nov 18, 2021 4:25 pm I heard an amazing math "trivia" question yesterday
A basketball player has a free-throw percentage of less than 75 percent early in the season.
By season's end, his free-throw percentage has risen to above 75 percent.
Is it necessarily true that his free-throw percentage was ever exactly 75 percent?
Re: Doug's Fiendish Trick Trivia Questions
X is time, Y is position
Day One is 0,0 to 1,1
Day Two is 0,1 to 1,0
These must intersect
Day One is 0,0 to 1,1
Day Two is 0,1 to 1,0
These must intersect
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Re: Doug's Fiendish Trick Trivia Questions
You can also imagine both trips taking place during the same day.
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Re: Doug's Fiendish Trick Trivia Questions
what if the rock is actually a teleporter and the positions aren't continuous
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Re: Doug's Fiendish Trick Trivia Questions
thanks, khaos
Re: Doug's Fiendish Trick Trivia Questions
got emRylinks wrote:thanks, khaos
Re: Doug's Fiendish Trick Trivia Questions
Of course I want to make it a trick question
A man sets off at dawn from the bottom of a mountain, and spends all day climbing to the top, arriving at sunset and spending the night. The next day, he sets off at dawn back down the mountain, and arrives back at the bottom of the mountain at sunset. Is it necessarily true that there is a time of day when he was in the exact same location on the path at the exact same moment of the day on both days?
A man sets off at dawn from the bottom of a mountain, and spends all day climbing to the top, arriving at sunset and spending the night. The next day, he sets off at dawn back down the mountain, and arrives back at the bottom of the mountain at sunset. Is it necessarily true that there is a time of day when he was in the exact same location on the path at the exact same moment of the day on both days?
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Re: Doug's Fiendish Trick Trivia Questions
possibly, but not necessarily, i think?groff_enthusiast wrote: ↑Mon Nov 22, 2021 3:23 pm A man starts walking up a mountain on a well worn path at 7:00AM. He reaches the top at nightfall and spends the night in a Cabin. The next day, he picks up a large rock as a memento and begins walking down at 7:00AM. Is there a time when was in the exact same location on the path at the exact same moment of the day on both days?
u gotta skate
Re: Doug's Fiendish Trick Trivia Questions
yeah that's why it was a fair copgroff_enthusiast wrote: ↑Mon Nov 22, 2021 3:26 pm
You were being quite precise, just not in the way you wanted.
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Re: Doug's Fiendish Trick Trivia Questions
oh neat
i wonder where my intuition went astray
u gotta skate
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Re: Doug's Fiendish Trick Trivia Questions
A memento is so you can remember; momentous means you'll never forget
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Well yeah, your memory keeps moving forward thanks to mementum
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Re: Doug's Fiendish Trick Trivia Questions
when britain mobilized for WW1, the colonels-in-chief of the 1st royal dragoons and the 1st king's dragoon guards did not report for duty. why not?
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That is wonderful
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Which weighs more, a pound of heavy cream or a pound of light cream
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Doug wrote:Which weighs more, a pound of heavy cream or a pound of light cream
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which has more letters, banana or pineapple
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That is fantastic. I've always used the notion that if you're not in a vacuum the feather weight is counting air.Jeb Bush 2012 wrote: ↑Sat Jan 08, 2022 2:30 amwhich weighs more, a pound of gold or a pound of feathersSpoiler!
Re: Doug's Fiendish Trick Trivia Questions
WellJeb Bush 2012 wrote: ↑Sat Jan 08, 2022 2:30 amwhich weighs more, a pound of gold or a pound of feathersSpoiler!
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How many horsepower is a horse?
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What sort of language test do you have to pass to join the French Foreign Legion?
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in chess, is it possible to reach the starting position except it's black's move instead of white?
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