Problem of the Week #26: Monday July 3rd, 2023 As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems. Please register for an account if you would like to join the discussion below or share your own problems.
Consider this family of popular puzzles: You have two empty water jugs with no markings. One holds exactly 8 liters of water when full, and the other holds 3 liters. You also have a full tub with an endless supply of water and another large unmarked empty jug of unknown volume. The goal is to measure out a given volume of water to put into the large jug using the other two jugs.
a). Is it possible to measure out 4 liters of water in the large jug using the two smaller ones?
b). Is it possible to measure out any whole number liters of water from 1 to 10 this way?
c). Is it possible to measure out any positive whole number liters of water this way?
d). How many times do we have to pour water between jugs to measure out 4 liters of water in the large jug?
e). What whole number volume of water from 1 to 10 liters takes the most number of times of pouring water between jugs to measure out?
f). How many ways are there to measure out 7 liters of water in the large jug?
g). If instead of an 8L and a 3L jug, we have an 8L and a 6L jug, which whole number liters of water would we not be able to measure out in the large jug?
h). What whole number volume of water from 1 to 10 liters takes the most number of times of pouring water between jugs to measure out using an 8L and a 6L jug?
i). Share your own problem inspired by this one.
j). Give one of these questions to a friend/colleague/student/family member to start a mathematical discussion.