Welcome to this month’s edition of Problems to Ponder! Pose them in your classroom as a challenge or try them out yourself. Have an interesting solution? Send it to thevariable@smts.ca for publication in a future issue of The Variable, our monthly periodical.
Climbing Snail
A snail is at the bottom of a 30 foot well. The snail climbs up 4 feet each day and slides down 3 feet each night. How many days does it take for the snail to get out of the well?
What if the snail climbs up 4 feet each day and slides down 2 feet each night? What if it climbs up k feet each day and slides down n feet each night?
Adapted from Coldwell, N. (n.d.). A collection of quant riddles with answers. Retrieved from http://puzzles.nigelcoldwell.co.uk/
Three Ants
Three ants are sitting at the three corners of an equilateral triangle. Each ant randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?
Extend to other shapes (e.g., square? octagon? n-sided polygon?).
Adapted from Coldwell, N. (n.d.). A collection of quant riddles with answers. Retrieved from http://puzzles.nigelcoldwell.co.uk/
Sweet and Sour
Suppose that an ant will always position itself so that it’s precisely twice as far from vinegar as it is from honey. If we put a dab of vinegar at a point A and a dab of honey at a point B and we release a troop of ants, what formation will they take up?
Adapted from Barbeau, E. (1995). After math. Toronto, ON: Wall & Emerson.
