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?
Write the first 10 prime numbers in a line. How can you remove 6 digits to get the largest possible number?
In one move, it is permitted to either double a number or to erase its last digit. Is it possible to get the number 14 from the number 458 in a few moves?
Find the largest six-digit number, for which each digit, starting with the third, is equal to the sum of the two previous digits.
Find the largest number of which each digit, starting with the third, is equal to the sum of the two previous digits.
Find a two-digit number that is 5 times the sum of its digits.
When we write 137 in decimal, we mean \(1 \cdot 10^2 + 3 \cdot 10 + 7 \cdot 1\). If we write it instead using powers of 2, we have \(137 = 1 \cdot 2^7 + 0 \cdot 2^6 + 0 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0\). To tell apart binary representation from decimals, we can use the following notation: \(137 = (10001001)_2\).
What is the number 273 in binary? Note that using binary is useful for finding whether a particular Nim game is a winning position or a losing position.