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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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?

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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).

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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?

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There are dominoes in the box. The figure shows only how the halves of the dominoes are arranged, but the borders are not shown. Determine how they pass.

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List all the four natural numbers giving a total of 15.

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A flock of one-headed centipedes and three-headed dragons was flying. Together they had 648 legs and 39 heads. How many legs does a dragon have?

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Cut the drawn figure into two identical (matching when superimposed) parts.

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There are 17 parallels and 24 meridians on the globe.
How many parts is the surface of the globe divided into?

ℹ️ Meridian is an arc connecting the North Pole with the South Pole.
Parallel is a circle parallel to the equator (the equator is also a parallel).

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Cut the board shown in the picture into 4 equal parts so that each of them contains exactly 3 shaded cells.

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Cut the figure shown in the figure into two parts, from which you can fold a triangle.

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Say there are 100 prisoners numbered 1 to 100. Slips of paper containing each of their numbers are randomly placed in 100 boxes in a sealed room. One at a time, each prisoner is allowed to enter the room and open any 50 of the 100 boxes, searching for their number. And afterwards, they must leave the room exactly as they found it, and they can't communicate in any way with the other prisoners. If all 100 prisoners find their own number during their turn in the room, they will all be freed. But if even one of them fails to find their number, they will all be executed. The prisoners are allowed to strategize before any of them goes into the room. So what is their best strategy?

🎞 In this video, popular science channel Veritasium's Derek Muller explains the riddle by putting the probability into perspective and dives deeper to make sure the viewers can understand it fully.

A quadrilateral with side lengths 1, 1, 1 and 2, two of which are parallel, is divided into four identical shapes. As a result, the upper side is divided into four segments. Find the ratio of the length of the larger segment to the smaller one.

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