- 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.

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.

Our solution:

Take a piece of fruit from the "apples and oranges" crate. If it's an apple then you know that is the "apples" crate since ALL THE CRATES ARE LABELED INCORRECTLY. This means the crate marked "apples" must be "oranges" and the crate marked "oranges" must be "apples and oranges".