Whoever finds a “set” here will receive a chocolate bar from me.
Set is a brilliant game that we played 5 years ago. Screams, screams, photographing combinations.
The rules of the game say it was invented in 1991 by geneticist Marsha Falco while taking notes during a 1974 study of epilepsy in German Shepherds. For those whose brains are exhausted enough by mathematics, after a while there is a suspicion that there are some echoes here with planimetry and drawing lines through points. (For given two cards, there is one and only one card that is in the same set with them.)
Marsha Falco seems to be asking: “Well, didn’t you find the “set”?”
Remembering the rules
Set is a card game. All cards have four parameters, each of which takes three values (total 3 x 3 x 3 x 3 = 81 cards).
The types and values of the parameters are as follows:
- shape ::= ellipse | rhombus | "snot"
- color ::= red | green | violet
- fill ::= white | striped | solid
- count ::= 1 | 2 | 3
Purpose of the game consists in finding special combinations of three cards. Three cards are called a “set” if, for each of the four attributes, the cards are either all the same, or all are different.
In other words, we can say that three cards will not make a set if two cards have one parameter value, and the third one has a different one. It can be seen that for any two cards there will always be a third (moreover, the only one) with which they will be a set.
Game progress: The host puts 12 cards on the table. When someone finds a set, they shout "Set!" and then calmly takes the constituent cards of the set. If there is no set in the laid out cards (most likely, it just seems that there is not), the host lays out three more cards.
The maximum number of cards without a set is 20. The round continues until the deck runs out. The one with the most sets wins.
Mathematicians fussed and presented a combination of 20 cards. Who considers himself Chuck Norris can forget this picture and try to assemble "solitaire" without a set on his own.
Or check, what if there is still a “set” here?
20 cards without a set
It is convenient to check that there is no "set by color".
The same cards, but the location shows what sets were carried by the "fill" parameter.
In count.
By figures.
There is no set for the difference of signs.
Open unsolved problem of mathematics
How many cards can be laid out in order not to get a single "set"? The sign has three meanings.
with 1 "sign" - 2 cards
2 signs - 4 cards
3 signs - 9 cards
4 signs - 20 cards
5 signs - 45 cards
6 signs - 112 cards
7 signs - xs
And when "n→∞"?
Video
Game creator:
Alexey Savvateev speaks effervescently about Seth:
Articles
Source: habr.com