A girl chose a 4-letter word and replaced each letter with the corresponding number in the alphabet. The number turned out to be 2091425. What word did she choose?
One three-digit number consists of different digits that are in ascending order, and in its name all words begin with the same letter. The other three-digit number, on the contrary, consists of identical digits, but in its name all words begin with different letters. What are these numbers?
Replace the question marks with the appropriate letters or words:
a) r, o, y, g, b, ?, ?;
b) a, c, f, j, ?, ?;
c) one, three, five, ?,
d) A, H, I, M, O, T, U, ?, ?, ?, ?;
e) o, t, t, f, f, s, s, e, ?, ?.
There are five chain links with 3 rings in each. What is the smallest number of rings that need to be unhooked and hooked together to connect these links into one chain?
In an apartment building in which there are only married couples with children, a population census was carried out. The person who conducted the census stated in the report: “There are more adults in the building than children. Each boy has a sister and there are more boys than girls. There are no childless families.” This report was incorrect. Why?
There are scales without weights and 3 identical in appearance coins, one of which is fake: it is lighter than the real ones (the real coins are of the same weight). How many weightings are needed to determine the counterfeit coin? Solve the same problem in the cases where there are 4 coins and 9 coins.
We have scales without weights and 3 identical in appearance coins. One of the coins is fake, and it is not known whether it is lighter or heavier than the real coins (note that all real coins are of the same weight). How many weighings are needed to determine the counterfeit coin? Solve the same problem in the cases where there are 4 coins and 9 coins.
On a table five coins are placed in a row: the middle coin shows heads and the rest show tails. It is allowed to turn over three adjacent coins simultaneously. Is it possible to get all five coins to show heads after turning the coins over several times?
In Wonderland, an investigation was conducted into the case of a stolen soup. At the trial, the White Rabbit said that the soup was stolen by the Mad Hatter. The Cheshire Cat and the Mad Hatter also testified, but what they said, no one remembered, and the record was washed away by Alice’s tears. During the court session, it became clear that only one of the defendants had stolen the soup and that only he had given a truthful testimony. So, who stole the soup?
Do you think that among the four consecutive natural numbers there will be at least one that is divisible a) by 2? b) by 3? c) by 4? d) by 5?