The most interesting thing is how some are proven to be the best, and others are just found to be one currently known best solution, but we were unable to prove it.
You just showed that 420 is the only possible solution if the sequence converges . It is still possible that that’s not the case. It must be shown separately that the sequence converges.
Not 1, but indeterminate. 0 raised to the power of any R ≠ 0 is is 0. Any R ≠ 0 raised to the poser of 0 is 1. So 0^0 might be 0 or 1, there's no way of determining which.
This is cool but definitely do not consider this a proof for the area of an ellipse. You can prove the area of a circle with the area of an ellipse by making the 2 radius the same but you definitely cannot go the other way around.
Great example of empathy, too. Without the ability to think about the others' perspectives, the 2nd prisoner would stay quiet indefinitely thinking he has a 1/3 chance of having one color and 2/3 for the other color.
Somethings wrong with the drive times in bc. There's a 2 hr ferry to get to Vancouver island not shown. And the roads accross southern bc don't enable N-S driving from the US
I think of it as “how many instances of this number are there?” In the case of 0^0 how many non-instances of 0 do you have? Well, you can only have 1 instance of something not being present.
Good problem man. An important step is missing tho: prove that the two radii form a straight line (the centers and intersection point are collinear). One way to do it: remember that radii are perpendicular to the tangent lines, and since both share the same tangent (because the circles are tangent), this implies that both radii form a straight line.
I guess mine wasn't as elegant (as now that I think back on it, it's more of a trial and error answer), but was much easier for me solve. I turned the equations into: 1. B(N+1) = 40 2. P(B+2) = 48 3. N+3P = 33 Then, what can B be where it is a factor of 40, but also adding two is still a factor of 48, of which there are three solutions (2, 4, and 10). I used the solution of B to figure out N in the first equation, plugged in N for the third equation and making sure that when I subtracted N from 33 I had a multiple of three, and using that to give me P, and using the second equation to make sure that P was also a factor of 48. Again, not as elegant, but took me about 2 minutes to do.
golden gate bridge to tahoe is 3.5 hours not sure how you got 5. I live in the Bay Area and used to commute to Tahoe every week and i can confirm it took a little over 3 hours.
If you sit down in an interview, nervous and stressed, and immediately gets this question right, you are probably overqualified for 99% of all amazon jobs.
Well, if number 1 and 2 had white hats, how would it work?, nr. 1 would still see a white and a black hat, meaning that he wouldnt be able to say anything, then nr. 2 would see the black hat in front of him and say white?! why?, theres still a 50/50 chance. That is assuming that nr. 1,2 and 3 couldnt see behind them. I dont understand, can someone help?
Swapping prisoner 1+4's hat is irrelevant. It's not about guessing the color of prisoner 1's hat, it's about guessing the color fo their own hat and prisoner 2's hat is still white.
