There are boys and girls sitting at the round table. Prove that the number of pairs of boy-girl and girl-boy neighbors is even.
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📜 Leaflet #alternation
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Mathematical proof
rigorous demonstration that a mathematical statement follows from its premises
A snail crawls along a plane at a constant speed, turning 90° every 30 minutes. Prove that it can return to its starting point only:
1) after an integer number of hours;
2) after an even number of hours.
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1) after an integer number of hours;
2) after an even number of hours.
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Snail
common name for shelled Gastropods
There are 8 rooks on the chessboard, of which no two beat each other. Prove that the number of rooks standing on the black fields is even.
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📜 Leaflet #alternation
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Chessboard
A chessboard is a game board used to play chess. It consists of 64 squares, 8 rows by 8 columns, on which the chess pieces are placed. It is square in shape and uses two colors of squares, one light and one dark, in a checkered pattern. During play, the board…
To a 17-digit number add a number written with the same digits, but in reverse order. Prove that at least one digit of the resulting sum is even.
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📜 Leaflet #alternation
There are 5 kinds of cups, 4 kinds of saucers, and 2 kinds of spoons in the "Everything for Tea" store. How many ways can you buy in this store:
1) a set of a cup, saucer, and spoon?
2) a set consisting of two different items?
📜 Leaflet #combinatorics
Wikipedia
1) a set of a cup, saucer, and spoon?
2) a set consisting of two different items?
📜 Leaflet #combinatorics
Wikipedia
Wikipedia
Combinatorics
branch of discrete mathematics