5

Part of 2019 India PRMO

Problems(2)

Simple Combinatorics on seating in a circle

Source:

Five persons wearing badges with numbers

1, 2, 3, 4, 5

5

chairs around a circular table. In how many ways can they be seated so that no two persons whose badges have consecutive numbers are seated next to each other? (Two arrangements obtained by rotation around the table are considered different)

Circular permutationsgeometrygeometric transformationrotation

Easy Division problem

Source: PRMO 2019 Leg 2 P5

N

be the smallest positive integer such that

N+2N+3N+\ldots +9N

is a number all of whose digits are equal. What is the sum of digits of

N

algebraDivisionnumber theory