Puzzle of the Week #6

by NM '20

Solvers of last week’s puzzle (in order):    
      1. Kate Ambrose
      2. Maggie Wang
      3. David Hla
      4. Mr. Rick DuPuy




NOTE: Due to initial errors in the problem, multiple answers seemed to be possible, and hence multiple were accepted. My apologies for the error. Additionally, no puzzle was published week because the puzzlemaker was out sick.
Answer to and commentary on Puzzle #5:
    Classification: Medium. The problem was intended to be the following:


    Obadiah wants Ezekiel and John to guess his birthday, and gives these possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17. Ezekiel knows the correct month, and John knows the correct day. Ezekiel says, "I don't know Obadiah's birthday, and I know John doesn't know." John says, "I didn't know at first, but I now know Obadiah’s birthday." Ezekiel says, "Now I also know!" When is Obadiah's birthday?

     This problem is an adaptation of the “Cheryl’s Birthday” problem that went viral a couple of years ago. Here’s a New York Times article that goes through the steps of the problem, and which should suffice for an answer explanation here; https://www.nytimes.com/2015/04/15/science/answer-to-the-singapore-math-problem-cheryl-birthday.html





Puzzle #6
NM (email redacted)

This week’s puzzle: Logic/Accounting. Jerome lives in Pumpkintown, South Carolina. With his four friends—Ambrose (Amb.), Augustine (Aug.), and Gregory (Gre.)—, Jerome wants to experiment with using pumpkin seeds as currency. So, one day, he, Amb., and Aug. decide to go to Gregory’s Jack o’ Lantern Emporium, where a local man called Basil is the cashier and Gre. is the manager. After perusing the Emporium’s shelves for a while, Jerome and his friend group decide to purchase one of the largest jack o’ lanterns, for which they pay 15 pumpkin seeds—5 each from Jerome, Amb., and Aug.. They hand the seeds to Basil, who starts walking over to the Seed Vault, where all pumpkin seed currency is kept. Gre. intercepts Basil and tells him to give 5 seeds back to the group because they’re friends of his. Basil obliges, but keeps 2 of the 5 seeds for himself—giving only 3 to Jerome, Amb., and Aug.. All go their separate ways, with Jerome et al. happy at the 3 seed rebate and Basil happy with his 2 seed plunder. However, Constantine, the store accountant, is baffled; having coyly watched the whole procedure, he realizes that Jerome et al. effectively paid 12 seeds (originally 15 minus the 3 seed rebate), and that Basil kept 2 of the 5 returned seeds for himself, summing to 14 seeds (12 for the Jerome group and 2 for Basil). However, the original payment was 15 seeds; what happened to the missing seed?