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NYC Love Triangle (Oct. 2021 Challenge Question)

Posted September 30, 2021 12:00 AM
Pathfinder Tags: challenge question

A woman who lives in Brooklyn has a boyfriend in Queens and another boyfriend in Manhattan. She loves them both equally.

She is a realtor with an unpredictable schedule. On Friday nights, she is torn between who to visit. So she allows the first subway train to arrive at her platform to decide who she will visit.

She decides to marry her Queens boyfriend when she realizes she is spending 86.6% of her weekends with him.

Why does this happen?

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#1

Re: NYC Love Triangle (Oct. 2021 Challenge Question)

09/30/2021 1:30 AM

The B train only operates during weekdays and shuts down fri night at around 9 o'clock

but the F train runs 24/7....So she would have to be at the station early to go to Manhattan, but she could go anytime to Queens...

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#2

Re: NYC Love Triangle (Oct. 2021 Challenge Question)

09/30/2021 5:39 AM

Both trains run every 10 minutes but the Queens train arrives on average 80.4 seconds before the Brooklyn train.

This means that her chances of catching the Queens train is 519.6s/600s = 0.866

Bonus question

How long does she have to date for to arrive at a figure 86.6% (correct to one decimal place)?

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#3
In reply to #2

Re: NYC Love Triangle (Oct. 2021 Challenge Question)

09/30/2021 8:25 PM

How long does she have to date for to arrive at a figure 86.6% (correct to one decimal place)?

I would say 1000 weeks to get 0.1% accuracy, a bit over 19 years.

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#4
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Re: NYC Love Triangle (Oct. 2021 Challenge Question)

10/01/2021 5:02 AM

I'm assuming that she's not doing any analysis just doing the calculation correct to 1 decimal place. What's the minimum number of weeks before she could get an answer of 86.6%?

Of course probability means that she'd be unlikely to hit that minimum.

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#5
In reply to #4

Re: NYC Love Triangle (Oct. 2021 Challenge Question)

10/01/2021 8:36 AM

I think she figured it out in hours as a percentage of the weekends....because she had an uncertain schedule that preempted some, if not most, weekends...

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#6
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Re: NYC Love Triangle (Oct. 2021 Challenge Question)

10/01/2021 11:41 AM

How long does she have to date for to arrive at a figure 86.6% (correct to one decimal place)?

I disagree with myself.

The answer can be found with this simple Matlab program:

(% = start of comment)

% <start of program>

a=1; % a = dates in Queens

b=1; % b = total weeks

v=0.866; % v = given ratio

while abs(a/b - v) >.0005 % repeat while the ratio is not close enough

if a/b < v % if it's too low, increase numerator

a=a+1;

else % else if too high, increase denominator

b=b+1;

endif

endwhile

printf('%d total weeks',b);

% <end of program>

% Answer 67 weeks, 58 (86.57%) spent in Queens

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#11
In reply to #6

Re: NYC Love Triangle (Oct. 2021 Challenge Question)

10/02/2021 5:02 AM

That's what I made it. I just used the slightly cheating way but more accessible to most.

B2 = =ROUND(0.866*A2)

C2 = =100*B3/A3

D2 = =ROUND(C3,1)

E2 = =D4-86.6

F2 = =IF(E2=0,1,0)

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#7

Re: NYC Love Triangle (Oct. 2021 Challenge Question)

10/01/2021 6:07 PM

The question is....

"Why does this happen?"

It happens because the girl finds out that she's 'with child' ... and according to the odds, it's the Queens guy what done it...

Yeah I think it was the other guy....

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#8
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Re: NYC Love Triangle (Oct. 2021 Challenge Question)

10/01/2021 6:41 PM