/sci/ - Science & Math

merry christmas fellow mathe/mg/cians
>>12504388
>>12504066
>>12504043

>>11011189
you can write E_i for the expected time if you start in seat i and want to end up in seat 2
then you get equations like this:
E_1 = 1 + 1/3( E_3 + E_4 + E_5)
basically the equation says if you want to go from 1 to 2, then you either go from 1 to 3, 4, 5 and continue from there
do the same for other starting points, this leaves you with linear system of 5 equations which you can easily solve.
There is also a subtlety: this system will have a solution, but also E_1 = ... = E_5 = +inf is a solution, considering the wording of the problem maybe you can ignore it, but normally you should think which case is right