A three-digit number \(ABB\) is given, the product of the digits of which is a two-digit number \(AC\) and the product of the digits of this number is \(C\) (here, as in mathematical puzzles, the digits in the numbers are replaced by letters where the same letters correspond to the same digits and different letters to different digits). Determine the original number.
Try to find all natural numbers which are five times greater than their last digit.
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?
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?
Fill the free cells of the “hexagon” (see the figure) with integers from 1 to 19 so that in all vertical and diagonal rows the sum of the numbers, in the same row, is the same.
Six sacks of gold coins were found on a sunken ship of the fourteenth century. In the first four bags, there were 60, 30, 20 and 15 gold coins. When the coins were counted in the remaining two bags, someone noticed that the number of coins in the bags has a certain sequence. Having taken this into consideration, could you say how many coins are in the fifth and sixth bags?
Using five twos, arithmetic operations and exponentiation, form the numbers from 1 to 26.
Using five threes, arithmetic operations and exponentiation, form the numbers from 1 to 39.
Using five fours, arithmetic operations and exponentiation, form the numbers from 1 to 22.