14
Problems(2)
6 rows of doors, both rows are made up of three doors
Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 2 E14
12/12/2022
In Durer’s duck school, there are six rows of doors, as seen on the diagram; both rows are made up of three doors. Dodo duck wishes to enter the school from the street in a way that she uses all six doors exactly once. (On her path, she may go to the street again, or leave the school, so long as she finishes her path in the school.) How many ways can she perform this?
Two paths are considered different if Dodo takes the doors in a different order.
https://cdn.artofproblemsolving.com/attachments/5/1/8b722eb2c642e8275928753921fdfbd7495df9.png
combinatorics
1^1+2^2+3^3+. . .+2021^{2021} mod 35
Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 2 E+14
12/12/2022
Benedek scripted a program which calculated the following sum: . What is the remainder when the sum is divided by ?
number theoryremainder