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

📜 Leaflet #cut2

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?

📜 Leaflet #balance

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.)

📜 Leaflet #balance

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?

📜 Leaflet #balance

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.

📜 Leaflet #balance

🎞 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.)

📜 Leaflet #balance

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

📜 Leaflet #balance

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?

📜 Leaflet #time

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.)

📜 Leaflet #time

The driver of a long-range truck looked at the instruments of his car and saw that the speedometer shows 25952. "What a beautiful number I drove. Probably, the next beautiful number will not fall out soon," he thought. However, after an hour and twenty minutes, the following beautiful number appeared on the speedometer. How fast was the truck going?

📜 Leaflet #time

There are two hourglasses: one for 5 minutes and one for 8 minutes. How can they be used to time 7 minutes?

📜 Leaflet #time

Cut the dial into two parts so that
1) the sum of the numbers in each part was the same;
2) the sum of the digits in each part was the same.

📜 Leaflet #time

How many times a day do the hands of the clock form a right angle?

📜 Leaflet #time

Lucas's alarm clock is ruined: he is in a hurry for 4 minutes an hour. At 7 p.m., Lucas set the exact time on it and set the call to 7 a.m. What time will Lucas wake up?

📜 Leaflet #time

James has 10 sticks 50 cm long. He wants to cut them so that 50 sticks with a length of 10 cm are obtained.
How many cuts will he have to make?

📜 Leaflet #different