Solution to Riddle of the Week

Solution to Riddle of the Week: A Shipment of Apples to Bananaville

Difficulty level: Hard

Michael Stillwell
 
By Jay Bennett

Obviously you cannot load up your truck with 1,000 apples and drive directly to Bananaville 1,000 miles away. All of your apples would go to the apple toll. You must devise a way to bring some apples part of the way, go back and get more, then get a full truckload to start with closer to Bananaville. You can see the original problem here.

SOLUTION

You can deliver a total of 833 apples to Bananaville. Let's see how.

First you depart Appleland with a full truckload of 1,000 apples and drive 333 miles, about a third of the way to Bananaville, and drop off the 667 apples you have left after tolls. Then you go back and repeat this process twice, which leaves you with 2,001 apples at the 333-mile mark.

The second leg of the journey is similar, but this time you will take two loads of 1,000 apples 500 miles further, which will give you 1,000 apples at the 833-mile mark with 167 miles still to go to Bananaville. (Alas, you must abandon one apple behind, for it will not fit into your truck.)

Finally, take the 1,000 apples you have left and drive the remaining 167 miles to Bananaville, arriving with 833 apples. The citizens of the noble town will surely thank you for adding a little variety to their diet.

You may have noticed a mathematical quirk to the solution. In the first step, you took three truckloads a third of the way (333 miles). But in the second step, you took two truckloads half of the overall distance (500 miles). This is the most efficient way to transport the apples because you leave yourself with the correct remaining number of apples for full truckloads, meaning products of 1,000. Because 1,000 miles doesn't cleanly divide by 3, you are forced to leave that one apple behind at the 333-mile mark of your journey.

It may have taken a bit more time than otherwise, but you have successfully brought the apple trade to Bananaville, and you paid as little as possible in apple tolls as well! Good work.