The monkey and the coconuts

Five men and a monkey were shipwrecked on an island. They spent the first day gathering coconuts. During the night, one man woke up and decided to take his share of the coconuts. He divided them into five piles. One coconut was left over so he gave it to the monkey, then hid his share, put the rest back together, and went back to sleep.

Soon a second man woke up and did the same thing. After dividing the coconuts into five piles, one coconut was left over which he gave to the monkey. He then hid his share, put the rest back together, and went back to bed. The third, fourth, and fifth man followed exactly the same procedure. The next morning, after they all woke up, they divided the remaining coconuts into five equal shares. This time no coconuts were left over.

How many coconuts were there in the original pile?

Can a month have a) 3; b) 4; c) 5; d) 6 Sundays?

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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?

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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?

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🎞 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?

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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?

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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.

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

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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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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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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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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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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?

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Wikipedia

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

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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.)

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

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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?

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