The term “experimental school” for about twenty years has ceased to be literal. The kids who go to these schools don’t even have special books schools no entirely new and radical method of teaching is tried there, while in the others, the supposedly non-experimental schools, one would proceed with an earlier system and make the necessary comparisons.

Nowadays, in my opinion, an experiment for a completely different school model here in Greece would be to test how much of the curriculum could be attributed to sources coming directly from the Internet. And to go even further, it would be worth looking for parents who would allow their children to be taught with material that only comes from the Internet.

It is certain that a day will soon come when employers will no longer ask if someone has a high school, high school or even elementary school diploma, but will choose the one whose knowledge is best suited for the job offered. So someone who hasn’t been to a school with teachers for a single day can get the job. It will not be good for society at all, because people with a completely one-sided (and one-sided) mentality will emerge, which we will have to prevent. How; Ultimately create an educational alloy where there will be a human-educator but with different tasks and powers compared to today. Rather than a bodyguard, it will be a facilitator and guide for various types of “knowledge packages” drawn mostly for free from the vast Internet.

In this way, new types of schools will inevitably appear, as has already begun to happen in other countries. It is well known that especially for Mathematics there are now so many addresses on the Internet where one can learn that one’s main problem will be where to start and how to proceed (so here too the enlightened guide is necessary). And it’s not just the now famous Chan Academy.

The reason for the above was given to me by the fact that during the holidays I came across a site dedicated to Geometry and aptly called “For Geometry Romantics”.

## Spiritual Gymnastics

**1.** Coming in May, what could be more appropriate than this: In a bouquet we put red, white and blue flowers. The sum of reds and whites is 100, while the sum of whites and blues is 53. Blues and reds are less than 53. How many of each kind do we have?

**2.** Ten bottles of pills are received from a pharmacist with a note from the company stating that in 9 bottles the pills weigh 5 grams each but in the tenth they weigh 6 grams each. He doesn’t know which bottle it is and instead of weighing one of each, he does something else and finds out which bottle it is in one weighing. How; If she is brought 6 bottles and told that more than one contains 6 gram pills, how will she know which ones by weighing them again?

## Answers to previous quizzes

**1.** These days, those who don’t have their own plane are forced to clog overbooked flights. In one, 100 people had tickets for 100 seats numbered accordingly on a flight. However, the first person to board the plane couldn’t find their ticket, and because of Easter, they were allowed to sit wherever they wanted. Other entrants would either find their own seat or sit in another if theirs was occupied by another passenger. What is the probability that the last person to enter is sitting in the place writing their ticket? If the first passenger chooses seat n°1, that is to say his own, and all the others take the seat indicated on their ticket, the last one too. But if the first seat in seat No. 100, the second will not sit in his seat. Now suppose that the first person is seated in seat 47. Then the passengers numbered 2 to 46 will sit in their seats. The passenger with ticket #47 must choose between seats 1, 100 or one above 47. If they choose #1, the last person will sit in their seat, #100. he chooses number 100, the last person will not sit in his place. If he chooses another which will be above No. 47, we use the same reasoning. We therefore arrive at the end that for the last there will have been either the n°1 or the n°100 with an equal probability, i.e. 50%, for each.

**2.** Two small boats carrying passengers and goods cross a river vertically at constant but different speeds. Each starting from a different bank at the start of the day, they meet at a distance of 720 meters from a bank. Arrived on the other side, everyone disembarks and after 10 minutes leaves for the other side. They now meet at a distance of 400 meters from the other bank, not the distance we measured before. How wide is the river? Let P be the width of the river. When they first met, they covered distances T of 720 and (Π-720) in the same period. If their speeds are for the slowest ship v1=(720/T) and v2=([(Π-720)/Τ)] for fastest, then (v2/v1)=[(Π-720)/720]. During their second encounter, the slowest ship traveled a distance (Π+400) and the fastest (2Π−400). So (v2/v1)=[( 2Π-400)/ (Π+400)]. We equalize and arrive at Π(Π-1760)=0. We reject Π=0, therefore Π=1760.

**Printed edition L’Étape**