NUMBER THEORY · LABORATORY
Jug laboratory: from coefficients to pours
Choose two integer capacities and an amount to isolate. Watch water and coefficients change one move at a time.
Based on Bonnie Averbach and Orin Chein’s method in Problem Solving Through Recreational Mathematics, p. 118 of the edition shown in the article; the display and cycles are our teaching extensions.
Read the article and method1. The mathematical check
All integer solutions
k is an integer. Coefficients are net counts, not the litres in individual jugs.
2. Choose a route
Each button tells you which jug to fill first. Both routes are valid, but they are not necessarily ordered from shortest to longest. Choose a button to restart at step zero and compare every move.
Zero target: both jugs are already empty. There is no second sequence of moves to perform.
Both strategies refill the pouring source and discharge the receiving jug. A move count does not automatically certify a minimum.
3. Watch one move at a time
Both jugs use the same scale in litres. Outline = capacity; colour = water present.
A ·
B ·
Automatic playback: one move per second. Pause and go back at any time.
State (A, B):
Balance verifiedTaken from the source
Returned to the drain
Total in the jugs
All steps and counters
| Step | Operation | State (A, B) | x | y | Total balance | Phase |
|---|