# A village with not enough resources

Village Morental
Population: 20
You: a visitor

The village doesn't have enough resources for 20 people. The king decides to ban 10 villagers from the village. The king is not ruthless, so he gives the villagers a chance to stay. He puts each of the 10 villagers in a cell with a button. The king arranged the cells in a row, so each villager has sight of the cells in front of him and sees if they are active or not. A cell can be either active or not active. If the cell is active the villager in the cell needs to press the button to deactivate it. If the button is clicked correctly the cell will open and the villager is free to go else he will be banned. From the outside you can see which cells are active and which are not.

Rules:
1) No one is allowed to talk during the trial but you.
2) You are just allowed to say either 'active' or 'not active' at the start of the trial, nothing else.
3) You're not allowed to do any movement.
4) The trial lasts 2 minutes. After this time every button, which hasn't been clicked, counts as not clicked.
4) Before the trial you have some time to talk to the villagers.

Note:
If a button is clicked you can clearly hear it being clicked.
If the rules are broken, all the villagers will be banned.

How can you keep all the villagers in the village?

• The good king tries to prevent an economic disaster, and some random visitor stops him, so eventually every villager will die from starvation... These days Thanos' idea seems fair. Commented Oct 7, 2019 at 7:58

You should agree with the citizens that

You say 'active' is the number of total active cells is even, and 'not active' if the total number if odd.

Then with the following strategy, everyone can stay in the village:

The last villager, who sees everyone else, has 10 seconds to press his button or not. He can clearly decide if he needs to press it, as he will see that his cell will have to make the total number of active cell even/odd (depending on what you said).

The next villager will hear if the one behind him pressed his button in the first 10 seconds. Then he has 10 seconds to decide if he presses his button: he sees everyone before him, knows if the one behind him pressed the button and the parity of the total active cells. Thus he can decide.

With this method, every citizen can decide correctly in 100 seconds.

• Nice one. Maybe too easy for you fellow puzzlers.
– Nati
Commented Oct 10, 2019 at 7:31