Problems(2)
max gcd of all 2022-digit numbers using only 1 and 7
Source: 2022 South Russian Girls MO - Assara Juniors p4
2/28/2024
Nadya has cards, each with a number one or seven written on it. It is known that there are both cards.Nadya looked at all possible -digit numbers that can be composed from all these cards. What is the largest value that can take the greatest common divisor of all these numbers?
number theorygreatest common divisor
twists in a periodic decimal fraction
Source: 2022 South Russian Girls MO - Assara Seniors p4
3/1/2024
Alina knows how to twist a periodic decimal fraction in the following way: she finds the minimum preperiod of the fraction, then takes the number that makes up the period and rearranges the last one in it digit to the beginning of the number. For example, from the fraction, she will get . What fraction will Alina get from fraction ?
number theoryalgebraperiodic decimal number