As the message contains one truth, the third says that the gold is in the second box, if it is to be true, then the first box message will also become true. So Gold cannot be in second and third boxes. Gold is in the first box.

A) 23 hours | B) 47 hrs 15 min |

C) 52 hrs 15 min | D) 22 hrs 15 min |

Explanation:

Since they can do 19 programs in 19 hours, Then 52 programs in 52 hours respectively.

And a 15 min interval

Total time they take to do 52 programs is 52 hours 15 minutes.

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.