Decision Support Puzzles for Applied Mathematicians
October 2013 - Mini Chutes and Ladders
Chutes and Ladders is a popular children’s game where players compete to move along a game board the fastest. It involves both hazard squares that can set you back a few spaces and some helpful squares that can move you forward a few spaces. A mini version of the game is displayed in Figure 1.
A player starts at the red “Start” square and finishes at the green “Finish” square. A player advances along the board by spinning a spinner that results in moving forward one to three squares.
If a player ends his turn on a Ladder (depicted by the blue ladder icon) he immediately moves upwards along the ladder. For example, if a player ends his turn on square 6, he would immediately move to square 11.
If a player ends his turn on a Chute (depicted by the orange slide) he immediately moves down the slide. For example, if a player ends his turn on square 7, he would automatically move to square 2.
A player wins the game when he lands on or passes the Finish square.
Question: What is the average number of turns needed to finish the game? (Please provide your answer with one decimal place.)
Send your answer to firstname.lastname@example.org by December 15th, 2013. The winner, chosen randomly from correct answers, will receive a Magic 8 Ball. Past questions can be found at puzzlor.com.