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Short tales - Sincere and lying

SHORT TALES

These are short tales with a narrator speaking in first person. 
The most different situations, sets and times are described: but there is always something that you should find out.

AT THE EAST FAIR
As I do every year, I was going to the east fair together with 3 friends
to buy livestock, when 64 of our coins fell down on the ground. I picked up 5 coins and, noticing the coins of the others, I suggested: “Antonio, which picked up most of them, should give to us exactly as many coins as each of us owns at the moment. Then Bernardo,  which picked up the most coins after Antonio, should do the same; then Cirillo and finally me. Everybody will keep the recieved coins as his own”. They all agreed, thinking that they would profit from it: but actually each of us just recieved 16 coins.
How many coins picked each of us up?

THE PROMOTIONAL CAMPAIGN
When I was 18 I was one of the people in charge of an association.  The head office was open every day, including weekends, and due to my studies, I was able to be there only one day every four. During a promotional campaign there was a big amount of work to be done, and I asked my sister to help out. She accepted and guaranteed her presence one day every five. She begun to work on the first Friday of March,  I begun on the first Saturday of the month. It is most curious that my sister and I worked together on the same day only once during that month and I am sure it was on a Monday.
On which day of the month did we work together?

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