Zooplus дополнение

Вчера, собирая оборудование, случайно разбил выигранную чашку. Пошёл на стенд Zooplus и они мне поменяли её. А кроме этого я обнаружил, что сегодня они выдают новые задачи.

☆ - за правильное решение выдавали сумку с барахлом:

100 coins lie on the floor, 10 on the tails side, 90 on the heads side. How to split them into two groups, so that each group would have the same number of heads up? You cannot see or feel the side of the coin.

☆☆ - за правильное решение выдавали чашку:

Interrogator had a soft spot for smart people, so he said to 100 prisoners - I like you folks, really, so I will give you a chance. Each of you will be interrogated in a room with one light bulb which you can turn on/off. I will not mess with it. You don't know in what order each of you will be interrogated. It will last forever, unless one of you says "we've all been interrogated". If you are right, all of you are free to roam around the country and do whatever you were doing before, otherwise I will kill you. Slowly...
Can prisoners free themselves? If so, how?

☆☆☆ - за правильное решение выдавали футболку:

Agnieszka has chosen two numbers greater than 1. She multiplied them and gave the result to Darek. Then she summed them and gave the result to Rafal.
Darek - I don't know what the numbers are.
Rafal - I knew you wouldn't know.
Darek - Ha! Now I know!
Rafal - Now I know too!
What are the numbers if their sum is smaler than 20?

Последнюю задачу я смог решить, только когда мне объяснили, что ограничение 20 не известно ни Дареку, ни Рафалу.