Questions

The construction of the world’s largest optical telescope has started in northern Chile, which is expected to begin operating in 2024. The Extremely Large Telescope (ELT) is being built by the European Southern Observatory (ESO) and will have a main mirror that is 39m in diameter. The telescope will be positioned on top of Cerro Armazones – a 3046-metre long mountain Chile. It will tackle a wide range of scientific challenges, including probing Earth-like exoplanets for signs of life, studying the nature of dark energy and dark matter, and observing the universe’s early stages to explore humans’ origins.

Jayaprakash Narayan was an Indian independence activist, theorist, socialist and political leader who is popularly known as Lok Nayak.

- 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.

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.