**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?*

**SOLUTIONS**

**AT THE EAST FAIR**

*Antonio 33, Bernardo 17 and Cirillo 9. Going backwards in the passages of coins, you’ll notice that at each passage the 3 people that aren’t giving out coins, **have half of the coins **b**efore the suddivision. This means that before my suddivision Antonio, Bernardo and Cirillo had each 8, I 64-(8×3)=40. **Before **Cirillo’s, Antonio and Bernardo had 4, I had 20 and Cirillo 64- (4+4+20)=36. **Before ** Bernardo’s, Antonio 2, Cirillo 18, I had 10 and **Bernardo **64- (2+18+10)=34. Finally, in the beginning, Bernardo had 17 coins, Cirillo 9, Antonio 64-(18+9+5)=33, and I had 5.*

**THE PROMOTIONAL CAMPAIGN**

*The 17th. If Friday was one of the first 6 days of the month and Saturday the next day, my sister and I would have worked together on a Wednesday after five days from Friday, which means at the most the 11th of the month. Besides that, we would have met again after 20 more days, which is not possible due to the given indications. The first day of the month must have been a Saturday, and so the first Friday was the 7th. This means that I was at the head office on the days 1, 5, 9, 13, 17, 21, 25 e 29, and my sister on the days 7, 12, 17, 22 and 27: we met at work on Monday the 17th.*