Easy math puzzles
Poll
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46 members have voted
May 9th, 2024 at 3:32:08 PM
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Quote: unJonNot sure this is optimal as feels like the kind of thing that should go to 1/e as bikes go to infinity but
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Since the total is 100 x a sum of reciprocals, the distance diverges as the number of cars approaches infinity
May 9th, 2024 at 3:44:58 PM
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Quote: ThatDonGuyQuote: unJonNot sure this is optimal as feels like the kind of thing that should go to 1/e as bikes go to infinity but
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Since the total is 100 x a sum of reciprocals, the distance diverges as the number of cars approaches infinity
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Yeah thought that was neat. I also did find an e in there.
Since it’s really just the harmonic series, an estimate of the distance with N motorcycles is 100 * ( ln(N) + Euler’s Constant)
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
May 9th, 2024 at 4:42:45 PM
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Quote: Gialmere
You have 16 motorbikes gathered together at the edge of a desert plain. Each bike has a rider and a full tank of gas. A bike can travel 100 kilometers on a full tank.
Using all 16 bikes as a team, how far can you get one of the bikes to travel across the desert?
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I get 338.0728993 miles.
I'll explain my answer if I'm right and nobody else already did.
Congratulations to UnJon for beating me on this one.
Here is my thinking.
Everyone should drive as far as they can until they get to some point where one biker can top off the other 15 bikers and be left with nothing. When will that be?
Divide his gas into 16 parts. 15 of those parts will eventually be divided to the other bikers. One part will be used up on the journey. The distance traveled on 1/16 of a tank is 100/16 km = 6.25 km. At that point, everybody will have 1-6.25/100 = 93.75% of a tank. If you take the remaining gas of one biker and divide it up among the other 15, each other biker gets 0.9375/15 = 6.25% of a tank, exactly enough to top off.
Then they repeat this, but divide a tank into 15 parts. That will get them an extra 6 2/3 miles. Then they split up the gas of one biker to top off.
In the end, the distance of the furthest biker is 100*(1/16 + 1/15 + 1/14 + ... + 1/1 ) = 338.0729 km.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
May 9th, 2024 at 4:55:48 PM
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The answer can also be found by taking 100 times the integral from zero to infinity of:
(1 - (1 - 1/e^(x/16))^16) / 16 =
100 * 2436559 / 720720 =~ 338.07
This formula would be useful for a high number of motorcycles
(1 - (1 - 1/e^(x/16))^16) / 16 =
100 * 2436559 / 720720 =~ 338.07
This formula would be useful for a high number of motorcycles
It’s all about making that GTA
May 9th, 2024 at 5:05:45 PM
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FYI your first answer is expressed in miles and your solution is a mix of miles and km.Quote: WizardQuote: Gialmere
You have 16 motorbikes gathered together at the edge of a desert plain. Each bike has a rider and a full tank of gas. A bike can travel 100 kilometers on a full tank.
Using all 16 bikes as a team, how far can you get one of the bikes to travel across the desert?
link to original post
I get 338.0728993 miles.
I'll explain my answer if I'm right and nobody else already did.
Congratulations to UnJon for beating me on this one.
Here is my thinking.
Everyone should drive as far as they can until they get to some point where one biker can top off the other 15 bikers and be left with nothing. When will that be?
Divide his gas into 16 parts. 15 of those parts will eventually be divided to the other bikers. One part will be used up on the journey. The distance traveled on 1/16 of a tank is 100/16 km = 6.25 km. At that point, everybody will have 1-6.25/100 = 93.75% of a tank. If you take the remaining gas of one biker and divide it up among the other 15, each other biker gets 0.9375/15 = 6.25% of a tank, exactly enough to top off.
Then they repeat this, but divide a tank into 15 parts. That will get them an extra 6 2/3 miles. Then they split up the gas of one biker to top off.
In the end, the distance of the furthest biker is 100*(1/16 + 1/15 + 1/14 + ... + 1/1 ) = 338.0729 km.
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It’s all about making that GTA
May 9th, 2024 at 5:30:01 PM
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It's nice to see Ace2 posting again, and it's not even a craps puzzle.
Have you tried 22 tonight? I said 22.
May 9th, 2024 at 5:42:36 PM
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I never thought of this before, but an intuitive way to define/calculate the Euler–Mascheroni constant is to take the integral from zero to infinity of (1 - (1 - 1/e^(x/n))^n) / n dx minus the integral from one to n of 1/x dx. It will equal the EM constant as n approaches infinity and will be quite accurate at lower nQuote: unJonQuote: ThatDonGuyQuote: unJonNot sure this is optimal as feels like the kind of thing that should go to 1/e as bikes go to infinity but
link to original post
Since the total is 100 x a sum of reciprocals, the distance diverges as the number of cars approaches infinity
link to original post
Yeah thought that was neat. I also did find an e in there.Since it’s really just the harmonic series, an estimate of the distance with N motorcycles is 100 * ( ln(N) + Euler’s Constant)
link to original post
Last edited by: Ace2 on May 9, 2024
It’s all about making that GTA
