Pi Day Puzzle
Here’s a Pi Day puzzler from MoMath:
You are at a river and have two empty containers, one capable of holding exactly π (= 3.14159…) quarts of water and the other capable of holding exactly 3 quarts of water.
How many transfers of water will it take you to get water in one container that is within 1% of a quart?
Click here to reveal the answer.
Answer: 13 transfers.
You fill the π-jar and then fill the 3-jar from the π-jar, leaving .14159 in the π-jar. You then pour the water out of the 3-jar and transfer .14159 to the 3-jar. Repeating this sequence again (two transfers) gets you 2 x .14159 in the 3-jar. Four more repetitions of the sequence (eight more transfers) later and you will have a .8495 in the 3-jar. Fill the π-jar one more time and pour it into the 3-jar, and you will have .99113 in the π-jar.
If you enjoyed this water-pouring problem from MoMath, check out the Mind Over Measure exhibit at the nation’s only Museum of Math at 11 East 26th St.