4
Problems(2)
vintage tram with boys and girls (2018 Auckland MO J4)
Source:
11/14/2021
A vintage tram departs a stop with a certain number of boys and girls on board. At the first stop, a third of the girls get out and their places are taken by boys. At the next stop, a third of the boys get out and their places are taken by girls. There are now two more girls than boys and as many boys as there originally were girls. How many boys and girls were there on board at the start?
algebra
2 player game with numbers <=2018 (2018 Auckland MO S4)
Source:
11/15/2021
Alice and Bob are playing the following game:
They take turns writing on the board natural numbers not exceeding (to write the number twice is forbidden).
Alice begins. A player wins if after his or her move there appear three numbers on the board which are in arithmetic progression.
Which player has a winning strategy?
combinatoricsgamewinning strategyArithmetic Progression