GeekDad Puzzle of the Week Solution: Math Trolls

Geek Culture

Nora made it successfully to her Grandmother’s house with at least 1000 berries, enough for quite a few pies. Here is the puzzle as presented earlier this week:

Nora is taking a trip to visit her Grandmother in northernmost New York State this week, to bring her some freshly picked berries. On the way there, she has to cross a total of 30 bridges, and under each of the these bridges lives a troll. (That’s how they roll in northernmost New York.) Each troll is aware of their bridge number, and either demands or gives berries based upon the rarest or most applicable description of their bridge. They demand or give berries according to the following schedule:

  • Trolls under odd numbered bridges demand half of your berries.
  • Trolls under even numbered bridges demand 20 berries.
  • Trolls under prime numbered bridges give you half again the number of berries you are carrying.
  • Trolls under perfect square numbered bridges demand a quarter of your berries.
  • Trolls under perfect cube numbered bridges give you the number of berries you are carrying, doubling your number of berries.

If trolls round up in their demands (i.e., if you have 57 berries at the foot of a bridge best described as odd numbered, you will cross it with 28 berries), what is the minimum number of berries Nora must start with so that she ends up with 1,000 berries when she arrives at her Grandmother’s house?

Nora and I thank you for a record number of solutions submitted this week! The most common way to solve this problem was to use Excel, and represent each bridge (numbered 1 through 30) as a row, and perform the appropriate function. The most common way to solve this puzzle incorrectly was to apply the wrong formula. Contrary to a few “solutions,” 30 is not odd, 2 most definitely is a prime, and 1 while odd, is neither prime nor a perfect square; for the purposes of this puzzle, the most apt description is that it is a perfect cube!

Another point of discussion was around the trolls, and how they rounded fractions of a berry. The puzzle mentioned that trolls rounded up in their demands; it turned out that whichever way they rounded when they gave berries (prime numbered bridges gave you half again your current count), the answer was the same.

Congratulations to Chris Nye for correctly describing Nora’s path, and for posting that she needed to start with 44 berries in her basket to end up with at least 1,000 at the end of the trip. For everyone else making ThinkGeek purchases this week, please feel free to use the code GEEKDAD72JL to receive a $10 discount on a purchase of $50 or more. Thank you once again for all of your submissions!

Liked it? Take a second to support GeekDad and GeekMom on Patreon!
Become a patron at Patreon!