Be the first to move your child-shaped playing piece from square one to square 100 on the Chutes and Ladders game board--but watch out! If you land on the square that shows you ate too much candy--Ouch!--you get a tummy ache and slide down a chute to a square a few numbers below. But if you end your turn on a good-deed square, such as helping sweep up a mess, you'll be rewarded by a ladder-climb up the board.
For the last couple of days, and continuing for the next few days, I have been and will be looking at each team in the NHL and identifying a couple of players in particular that fit into one of two categories based on the once popular kids game, Chutes and Ladders. The players in the “chutes” category will be players who exceeded expectations last season, and will have a difficult time avoiding a slide in the coming season. The “ladder” category will consist of players who are ready to climb a level in their play and step up a notch. Feel free to brows back to see previous teams, and look for more teams in the coming days.
Having studied mathematics, I absolutely agree with you. Your informal explanation here could be easily translated to what we call an induction proof. If I remember later today, I’ll write out the formal proof where I believe I’ll be able to show that for any number strictly greater than 5 (n>5), there exists a possible chutes and ladders game where the winning player makes that number of moves.
The possibilities in chutes and ladders of course go to four repeated series of rolls for both players, and beyond. At first glance it might seem as if we can extend this sequence to the — literally infinitesimal — possibility of both players being stuck in an infinite loop by repeatedly throwing the same series of numbers. And any series of consecutive numbers that ends in infinity must logically have an infinite number of entries, thus making the answer to the original question “there’s an infinite number of different chutes and ladders games.”
Jim Maclean descends on Chutes and Ladders