5

Part of 2014 Tournament of Towns.

Problems(2)

TOT 2014 Spring O J5, Ali Baba and 40 thieves, one boat can carry 2 or 3

Source:

Ali Baba and the

40

thieves want to cross Bosporus strait. They made a line so that any two people standing next to each other are friends. Ali Baba is the first, he is also a friend with the thief next to his neighbour. There is a single boat that can carry

2

3

people and these people must be friends. Can Ali Baba and the

40

thieves always cross the strait if a single person cannot sail?

TOT 2014 Spring A J5, bw points, positive inegers on segments

Source:

There are several white and black points. Every white point is connected with every black point by a segment. Each segment is equipped with a positive integer. For any closed circuit the product of the integers on the segments passed in the direction from white to black point is equal to the product of the integers on the segments passed in the opposite direction. Can one always place the integer at each point so that the integer on each segment is the product of the integers at its ends?

combinatoricsColoring