Rabbit, getting ready for his guests, hung a light bulb in the three corners of his polygonal hole. When Winnie the Pooh and Piglet came to him, they saw that not all the pots of honey were lit. When they reached for the honey, two of the light bulbs broke. Rabbit moved the remaining bulb to a certain corner so that the whole burrow was illuminated.
Could this be?

📜 Leaflet #yes_or_no

The fox and the two little bears share 100 candies. The fox divides the candy into three piles; the lot determines who gets which. The fox knows that if the cubs get different amounts of candy, they will ask her to equalize their piles, and then she will take the excess for herself. Then everyone eats the candy they get.

1) Think of a way for the fox to put the candy in piles so that she eats exactly 80 candies (no more, no less).
2) Can the fox make it so that she eats exactly 65 candies?

📜 Leaflet #yes_or_not

🎞 CyberOne's stage debut with Lei Jun! Enjoy watching!

Baron Munchausen, returning from his round-the-world voyage, tells us that he crossed the border of Trapezundia exactly seven times on the way. Should we trust his words?

📜 Leaflet #alternation

In the jungle on his round-the-world voyage, Munchausen was attacked by panthers. As he dashed past two of them, they lunged at him, missed and mauled each other. Munchausen repeated this maneuver again and again until they all ate each other. According to Munchausen there were 97 panthers in all. Is this true?

📜 Leaflet #alternation

The grasshopper jumps in a straight line 1 meter to the left or to the right each time. After some time he is at the starting point. Prove that he has made an even number of jumps.

📜 Leaflet #alternation

All dice with "blanks" have been discarded from the domino set. Can the remaining dice be placed in a row according to the rules?

📜 Leaflet #alternation

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.

📜 Leaflet #alternation

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.

📜 Leaflet #alternation

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.

📜 Leaflet #alternation

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.

📜 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

Let's call a natural number "cute" if only even digits occur in its record. How many four-digit "cute" numbers are there?

📜 Leaflet #combinatorics

A soccer team needs to choose a captain and a deputy captain. How many ways can this be done? (There are 11 players on the soccer team.)

📜 Leaflet #combinatorics

There are 25 students in the class. How many ways can you choose two people to be on duty?

📜 Leaflet #combinatorics

The alphabet of the Mumbo Yumbo tribe consists of three letters: A, B and C. A word is any sequence of no more than 4 letters. How many words are there in the Mumbo Yumbo language?

📜 Leaflet #combinatorics

The menu in the school cafeteria does not change and consists of 10 dishes. For a change Oliver wants to order every day a set of dishes that he has never ordered before (the number of dishes does not matter, he can order all 10 dishes, or he can order only one, or none at all). How many days can he eat like that?

📜 Leaflet #combinatorics

Write out all sets of three digits, each of which is equal to 1, 2 or 3, if the order of the digits is unimportant (i.e. sets 112 and 121 are considered the same).

📜 Leaflet #trying_options

Wikipedia

The box contains blue, red, and green pencils. There are 20 in all. There are 6 times as many blue pencils as green pencils, and fewer red pencils than blue. How many red pencils are in the box?

📜 Leaflet #trying_options