Lucas borrowed $19 from James, pledging to return it within 4 months. Moreover, every month the amount of payment should grow, amount to an integer number of dollars and be completely divided by the amount of payment in the previous month.
How much will Lucas pay in the last month?

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Find the largest natural number, any two consecutive digits of which form an exact square.

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Winnie-the-Pooh and Piglet came out of their houses to meet each other and met 2 minutes later. After what time will Piglet come to Pooh's house if the speed of Winnie-the-Pooh is twice the speed of Piglet?

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Winnie the Pooh came out of the guests from Christopher Robin 1 minute later than Piglet. After what time will he catch up with Piglet if his speed is twice the speed of Piglet?

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Tigger and Winnie the Pooh went to visit Christopher Robin. At first Tigger ran twice as fast as Winnie-the-Pooh, but after half the way, he suddenly got tired and crawled the rest of the way at half the speed of Winnie-the-Pooh. Who met Christopher Robin first, Tigger or Winnie the Pooh?

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Tigger knows how to run at 30 kilometers per hour and really wants to learn how to spend one less minute per kilometer. At what speed should Tigger learn to run?

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Stubborn Winnie the Pooh decided to walk to the North Pole. At 12 o'clock Christopher Robin caught up with him on his bicycle and drove him to the place where it was the same distance to the North Pole as Winnie had already walked. Winnie-the-Pooh was at the North Pole at 14 hours. How long will it take Winnie the Pooh to get back on foot if you know that he was carried on a bicycle at twice the speed he walks?

Olivia and Emma were doing homework. Each of them started with mathematics, then learned a poem, then read the text in English, and finally completed an exercise in physics. For each subject, Olivia took half as much time as the previous one, and Emma took 4 times less time than the previous one. They started and finished at the same time. What did Emma do when Olivia took up physics?

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Two are running at different speeds down the subway escalator. Which of them will count more steps, who runs faster, or who runs slower?

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One day a snail crawled to the top of a bamboo, which grows so that each of its points rises up at the same speed. The way up took the snail 7 hours. After resting on top of the bamboo for exactly an hour, she descended to earth in 8 hours. How many times is the snail's speed greater than the bamboo's growth rate (both speeds are constant)?

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A simple problem with a somewhat unexpected answer.

Alice has two coins and Ben has three. They toss all their coins at the same time. The one with more eagles wins, and if it is the same, Alice wins. What is her probability of winning?

Solve the rebus: TIC+TAC=ACT. Letters are encoded numbers. The same letters mean the same digits, different letters mean different digits.

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Using each of the digits 1, 2, 3, 4 exactly twice, write an eight-digit number with exactly one digit between the ones, exactly two digits between the twos, exactly three digits between the threes, and exactly four digits between the fours.

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William, Oliver and James were solving problems. William said: "I have solved the most problems." Oliver doubted: "Either you didn't decide the most, or James decided the least." James said: "I've solved more problems than Oliver."
Who solved the most problems if only one of the boys is right?

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At the moment 1 dollar is worth 3 shekels 55 agorot.
How many dollars is 1 shekel worth?

ℹ️ A shekel is worth 100 agorot.
A dollar consists of 100 cents.
If the number of cents is not whole, it is rounded upwards.

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Five people took turns eating the cake. The first ate a fifth of it, the second ate a quarter of it, the third ate a third of the new leftover, the fourth ate half of what was left after the third, and the fifth finished the cake all the way.
Which one ate the most?

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There are 1,000 inhabitants of Cissylvania. Three of them are vampires, but few know which ones. A visiting writer, Mr. Stocker, asked each resident to name two people he thought were vampires. Each vampire named two other vampires, and the others could name whomever they wanted. Prove that, using the data from the survey (and knowing that there are exactly three vampires in Cissylvania), Mr. Stocker could choose a guide who is not a vampire.

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Seven teams participated in the one-round soccer tournament (each team played exactly one match against each other). At the end of the tournament, the top-ranked teams scored exactly half of the points. Could there have been exactly 6 draws at the end of the tournament? (3 points are given for a win, 1 for a draw and 0 for a loss).

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The grandfather is 56 years old and the grandson is 14.
In how many years will the grandfather be twice as old as the grandson?

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