Questions

India’s first smartcard-based Public Bicycle Sharing (PBS) initiative has launched in Mysuru, Karnataka on June 4, 2017. The cost of the project, partly funded by World Bank’s Global Environmental Facility, for the next six years is Rs 20.5 crore, covering the maintenance of the docking stations and bicycles. About 450 bicycles will be available for public use in the city. To rent a bicycle, the citizens of Mysuru or tourists need to register themselves either online or by visiting one of the six registration centres situated close to tourism centres and obtain a smart card after paying Rs. 350, including a refundable deposit of Rs. 250. Though the use of the bicycle is free for the first one hour, the users will have to pay a nominal fee of Rs. 5 for two hours, Rs. 10 for three hours and so on.

The Economic Survey for 2016-17, which is recently tabled by Finance Minister Arun Jaitley in Parliament, has expected India’s GDP growth estimation to be in 6.75 % to 7.5% for Financial Year 2017-18.

Our solution:

Toss the coin twice.
Let TH, HT and TT correspond to the three choices.
And if you get HH, just repeat (so it takes 8/3 tosses on average).


BIASED COIN

If the coin was biased, TH and HT would occur with equal probability.
So you could assign THHT, HTTH and THTH to the three choices, with other 4-toss outcomes rejected.
Or you could assign HTT, THT and TTH to the three choices, with other 3-toss outcomes rejected.

- Send the box with the lock to Alex. 

- Alex can't open it, but can put another lock on the box. 

- Alex sends this box with the 2 locks back to you, you unlock your lock and send it back to Alex again.

- So there is just Alex's lock on the box and Alex can now open it.