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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Cut the figure shown in the picture into four parts, and make a square out of them.

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Autumn colors 🍂

1) Is it possible to cut a chessboard into 1×2 dominoes?

2) And if one corner square was cut out of the chessboard, is it possible to cut?

3) And if two cells were cut out: the lower left and the upper left?

4) And if the lower left and upper right?

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There are three coins. Among them is a fake one that weighs less than the real one. How can you determine the counterfeit coin with a single weighing?

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Wikipedia

Among the 101 coins there is one fake, which differs in weight from the real one. But this time it is not known which way. In two weighings, determine whether the fake coin is lighter or heavier than the real one. (The coin itself does not need to be determined.)

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There are four weights. One of them is large and heavy, the second is smaller and lighter, the third is even smaller and lighter, and the fourth is the smallest and lightest. The weights are placed on the scales in turn (each time any of the weights is taken and placed on any cup of the scales). Is it possible, not knowing the exact weight of the weights, to put them all on the scales one by one in such an order that first three times the left cup is outweighed, and the last time the right one?

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There are five coins. There are three real coins, one fake coin that weighs more than the real coin, and one fake coin that weighs less than the real coin. In three weighings, identify both counterfeit coins.

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🎞 Toy models — small mathematics in a big world — Tadashi Tokieda

In 9 bags there are real coins (10 g each), and in one fake (11 g). With one weighing on a two-cup scale with an arrow, determine which bag the counterfeit coins are in. (The arrow shows how much the weight of coins on the "heavy" cup is greater than on the "light" one.)

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There are 64 coins, all different in weight. For no more than 94 weighings, determine the lightest and heaviest coins.

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At 4 o'clock in the afternoon, 6 seconds elapsed from the first to the last beat of the clock. How much time will pass from the first to the last beat at noon?

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On the clock that runs exactly, all the numbers have come off. Only the divisions without signatures remained. How do I know where to return each digit? (You don't have any other watches.)

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