Question 13
Alan and Benjie use the staircase shown in the diagram below to play a game
where the goal is to reach a certain level on the staircase first. At the beginning,
both of them will start in step 1, and in each turn, they will be playing the “Rock,
Paper and Scissors” game to move around the staircase. The winner in each game
gets to move 4 consecutive steps upward (or downward or a combination of both)
for showing a rock; 5 consecutive steps for showing scissors and 6 consecutive
steps for showing a paper. So, for example, when someone reaches step 10, he
must go down to the step 9 and so on, finally returning to the step 1 and then
goes back up doing the same procedure again until somebody wins. To illustrate
further, when a person shows a rock on the first game and wins and then in the
second game shows a paper and wins, he will then move and land on step 9.
Since Alan is curr ently on step 1 of the stairs, what is the least number of times
he has to win in order to reach step 2? Note: If a game is a tie (where both
players show the same hand, i.e. paper and paper), then they don’t move.
where the goal is to reach a certain level on the staircase first. At the beginning,
both of them will start in step 1, and in each turn, they will be playing the “Rock,
Paper and Scissors” game to move around the staircase. The winner in each game
gets to move 4 consecutive steps upward (or downward or a combination of both)
for showing a rock; 5 consecutive steps for showing scissors and 6 consecutive
steps for showing a paper. So, for example, when someone reaches step 10, he
must go down to the step 9 and so on, finally returning to the step 1 and then
goes back up doing the same procedure again until somebody wins. To illustrate
further, when a person shows a rock on the first game and wins and then in the
second game shows a paper and wins, he will then move and land on step 9.
Since Alan is curr ently on step 1 of the stairs, what is the least number of times
he has to win in order to reach step 2? Note: If a game is a tie (where both
players show the same hand, i.e. paper and paper), then they don’t move.